\(104=2+3+4+5+6+7+8+9+10+11+12+13+14\) (som van opeenvolgende gehele getallen)

\(104=6+8+10+12+14+16+18+20\) (som van opeenvolgende pare getallen)

\(104\mathbf{\color{blue}{\;=\;}}23+25+27+29\mathbf{\color{blue}{\;=\;}}51+53\) (som van opeenvolgende onpare getallen)

\(104=((0;0;2;10)\,(0;2;6;8)\,(4;4;6;6))\lower2pt{\Large{\color{teal}{➋}}}\to\{\#3\}\)

\(104=((0;0;0;2;2;2;2;2;4)\,(0;1;1;1;1;1;2;3;4))\lower2pt{\Large{\color{teal}{➌}}}\to\{\#2\}\)

\(104=4!+4^2+4^3\)

\(104\mathbf{\color{blue}{\;=\;}}2^2+10^2\mathbf{\color{blue}{\;=\;}}[3^6][9^3][27^2]-[5^4][25^2]\mathbf{\color{blue}{\;=\;}}[9^3][27^2]-25^2\mathbf{\color{blue}{\;=\;}}15^2-11^2\mathbf{\color{blue}{\;=\;}}30^3-164^2\mathbf{\color{blue}{\;=\;}}42^3-272^2\mathbf{\color{blue}{\;=\;}}\)

104.1

\(104\mathbf{\color{blue}{\;=\;}}\)(som van drie derdemachten)

\(\qquad~~~~\)References Sum of Three Cubes

\(\qquad~~~~\)Getallen van de vorm \(~9m+4~\) of \(~9m+5~\) kunnen nooit als som van drie derdemachten geschreven worden.

\(\qquad~~~~\)In dit geval is \(m=11~~(+5)\).

\(104\mathbf{\color{blue}{\;=\;}}\)(som van vier derdemachten)

\(\qquad~~~~(z\gt1000)\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-1)^3+(-4)^3+(-7)^3+8^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{5^3+11^3+14^3+(-16)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{2^3+14^3+20^3+(-22)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-4)^3+(-22)^3+(-28)^3+32^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{17^3+(-25)^3+(-28)^3+32^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{14^3+(-19)^3+(-37)^3+38^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{11^3+(-43)^3+(-46)^3+56^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-16)^3+32^3+68^3+(-70)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{5^3+(-28)^3+(-85)^3+86^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{41^3+(-46)^3+(-97)^3+98^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{5^3+(-49)^3+(-97)^3+101^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{77^3+(-88)^3+(-100)^3+107^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-31)^3+47^3+110^3+(-112)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{20^3+83^3+98^3+(-115)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-10)^3+(-79)^3+(-106)^3+119^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-70)^3+104^3+104^3+(-124)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{50^3+62^3+119^3+(-127)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-22)^3+(-88)^3+(-112)^3+128^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{44^3+68^3+125^3+(-133)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{20^3+(-43)^3+(-154)^3+155^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{26^3+86^3+161^3+(-169)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-4)^3+56^3+170^3+(-172)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{119^3+(-127)^3+(-172)^3+176^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{89^3+(-124)^3+(-169)^3+182^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-85)^3+104^3+182^3+(-187)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{98^3+134^3+152^3+(-190)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-130)^3+164^3+182^3+(-202)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-4)^3+98^3+194^3+(-202)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-10)^3+(-154)^3+(-172)^3+206^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{140^3+146^3+158^3+(-214)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-76)^3+(-100)^3+(-214)^3+224^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{125^3+155^3+227^3+(-259)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-4)^3+116^3+251^3+(-259)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{41^3+194^3+224^3+(-265)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{59^3+(-187)^3+(-232)^3+266^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-109)^3+(-124)^3+(-280)^3+293^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{38^3+(-205)^3+(-259)^3+296^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{77^3+203^3+287^3+(-319)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-64)^3+(-106)^3+(-346)^3+350^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{38^3+281^3+287^3+(-358)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{110^3+(-238)^3+(-328)^3+362^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{128^3+(-154)^3+(-358)^3+362^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-46)^3+98^3+374^3+(-376)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-133)^3+149^3+398^3+(-400)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-52)^3+104^3+404^3+(-406)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{77^3+185^3+395^3+(-409)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-46)^3+(-187)^3+(-406)^3+419^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{14^3+194^3+410^3+(-424)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{62^3+(-262)^3+(-400)^3+434^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{227^3+(-259)^3+(-430)^3+440^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{5^3+287^3+401^3+(-445)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{134^3+(-316)^3+(-406)^3+458^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-28)^3+(-85)^3+(-460)^3+461^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{197^3+203^3+440^3+(-466)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{92^3+164^3+461^3+(-469)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-64)^3+176^3+461^3+(-469)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{122^3+131^3+518^3+(-523)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-70)^3+356^3+488^3+(-544)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-16)^3+(-154)^3+(-550)^3+554^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-259)^3+(-352)^3+(-517)^3+584^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{332^3+(-436)^3+(-556)^3+602^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{527^3+(-550)^3+(-583)^3+602^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-358)^3+380^3+608^3+(-616)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{134^3+(-259)^3+(-613)^3+626^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-220)^3+236^3+644^3+(-646)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{71^3+182^3+650^3+(-655)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-67)^3+(-100)^3+(-658)^3+659^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{14^3+362^3+626^3+(-664)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{296^3+(-301)^3+(-667)^3+668^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{89^3+308^3+647^3+(-670)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-196)^3+470^3+593^3+(-673)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-22)^3+224^3+680^3+(-688)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-256)^3+(-406)^3+(-628)^3+692^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{392^3+(-496)^3+(-646)^3+692^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-136)^3+362^3+668^3+(-700)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-112)^3+(-382)^3+(-670)^3+710^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{212^3+(-322)^3+(-697)^3+713^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-241)^3+560^3+593^3+(-718)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{326^3+467^3+644^3+(-739)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-46)^3+515^3+644^3+(-739)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{230^3+362^3+704^3+(-742)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-280)^3+506^3+692^3+(-760)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{14^3+(-304)^3+(-757)^3+773^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-154)^3+266^3+791^3+(-799)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-22)^3+392^3+776^3+(-808)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-19)^3+(-589)^3+(-700)^3+818^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-13)^3+(-403)^3+(-784)^3+818^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{116^3+248^3+833^3+(-841)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{173^3+419^3+812^3+(-850)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-508)^3+(-535)^3+(-697)^3+854^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-322)^3+(-625)^3+(-706)^3+857^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{212^3+524^3+794^3+(-868)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-436)^3+455^3+866^3+(-871)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-463)^3+(-643)^3+(-673)^3+875^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{14^3+(-544)^3+(-802)^3+878^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-502)^3+584^3+854^3+(-886)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-4)^3+(-574)^3+(-802)^3+890^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-445)^3+(-637)^3+(-715)^3+893^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{698^3+(-778)^3+(-838)^3+896^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{482^3+(-514)^3+(-886)^3+896^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-43)^3+410^3+875^3+(-904)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-136)^3+245^3+899^3+(-904)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-454)^3+(-658)^3+(-718)^3+908^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-154)^3+206^3+920^3+(-922)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{728^3+(-739)^3+(-916)^3+923^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-391)^3+734^3+791^3+(-940)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{140^3+(-358)^3+(-940)^3+956^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-274)^3+(-742)^3+(-844)^3+1010^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{20^3+(-385)^3+(-991)^3+1010^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{236^3+(-784)^3+(-886)^3+1052^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-217)^3+(-727)^3+(-940)^3+1070^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-22)^3+(-850)^3+(-904)^3+1106^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-721)^3+(-814)^3+(-922)^3+1193^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~(z\gt1000)\)

\(104\mathbf{\color{blue}{\;=\;}}\)(som van vijf vijfdemachten)

\(\qquad~~~~\bbox[lightyellow,3px,border:1px blue solid]{~oplossing~onbekend~}\mathbf{\color{blue}{\;=\;}}(z\gt200)\)

104.2

\(104\mathbf{\color{blue}{\;=\;}}(1^2+1^2)*(4^2+6^2)\mathbf{\color{blue}{\;=\;}}(2^2+2^2)*(2^2+3^2)\)

104.3

\(104^2=17^3+24^3-89^2\)

\(104^2\mathbf{\color{blue}{\;=\;}}10816\mathbf{\color{blue}{\;=\;}}(108-\sqrt{16})^2\)

104.4

\(104^2\mathbf{\color{blue}{\;=\;}}[2^{15}][8^5][32^3]-28^3\mathbf{\color{blue}{\;=\;}}40^2+96^2\mathbf{\color{blue}{\;=\;}}112^2-12^3\mathbf{\color{blue}{\;=\;}}130^2-78^2\mathbf{\color{blue}{\;=\;}}185^2-153^2\mathbf{\color{blue}{\;=\;}}221^2-195^2\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\,\,346^2-330^2\mathbf{\color{blue}{\;=\;}}680^2-672^2\mathbf{\color{blue}{\;=\;}}1354^2-1350^2\mathbf{\color{blue}{\;=\;}}2705^2-2703^2\mathbf{\color{blue}{\;=\;}}5512^2-312^3\)

\(104^3\mathbf{\color{blue}{\;=\;}}13^5+91^3\mathbf{\color{blue}{\;=\;}}105^3-181^2\mathbf{\color{blue}{\;=\;}}208^2+1040^2\mathbf{\color{blue}{\;=\;}}260^3-4056^2\mathbf{\color{blue}{\;=\;}}312^3-5408^2\mathbf{\color{blue}{\;=\;}}592^2+880^2\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\,\,1092^2-260^2\mathbf{\color{blue}{\;=\;}}1170^2-494^2\mathbf{\color{blue}{\;=\;}}1183^2-65^3\mathbf{\color{blue}{\;=\;}}1344^2-88^3\mathbf{\color{blue}{\;=\;}}1560^2-1144^2\mathbf{\color{blue}{\;=\;}}1833^2-1495^2\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\,\,2325^2-2069^2\mathbf{\color{blue}{\;=\;}}2808^2-2600^2\mathbf{\color{blue}{\;=\;}}4458^2-4330^2\mathbf{\color{blue}{\;=\;}}\bbox[2px,border:1px brown dashed]{5460^2-5356^2}\mathbf{\color{blue}{\;=\;}}8820^2-8756^2\)

104.5
\(104\) als resultaat met breuken waarin de cijfers van \(0\) tot \(9\) exact één keer voorkomen : (\(3\) oplossingen) :
\(614328/5907=618072/5943=823056/7914=104\) 		104.6
Men moet \(104\) tot minimaal de \(38370\)ste macht verheffen opdat in de decimale expansie exact \(104\) \(104\)'s verschijnen.
Terloops : \(104\)\(^{38370}\) heeft een lengte van \(77394\) cijfers.
104.7
\(104\) is op vijf verschillende wijzen de som van twee priemgetallen.

$$ 2~odd~primes \left[ \begin{matrix} &3&+&101\\ &7&+&97\\ &31&+&73\\ &37&+&67\\ &43&+&61 \end{matrix} \right. $$

104.8

Als som met de vier operatoren \(+-*\;/\)
\(104=(26+1)+(26-1)+(26*1)+(26/1)\)

104.9

\(3\)\(^{104}\)\(~=~41745579179292917813953351511015323088870709282081\) is de hoogst gekende macht van \(3\) waarbij

geen cijfer \(6\) voorkomt in de decimale expansie. (OEIS A131616)

104.10

Voor \(n=104~~\) geldt \(~~{\large\phi}(n)={\large\phi}(n+1) ~~\to~~ {\large\phi}(104)={\large\phi}(105)=48~~~~({\large\phi}\) of  'phi' staat voor totiënt)

Zie ook bij en   (OEIS A001274)

104.11

Voor \(n=104~~\) geldt \(~~{\large\sigma}(n)={\large\sigma}(n+12) ~~\to~~ {\large\sigma}(104)={\large\sigma}(116)=210~~~~({\large\sigma}\) of  'sigma' staat voor som der delers)

\(104\) is de tweede oplossing uit (OEIS A015882)

104.12

\(\begin{align}104\mathbf{\color{blue}{\;=\;}}\left({\frac{4}{3}}\right)^3+\left({\frac{14}{3}}\right)^3\mathbf{\color{blue}{\;=\;}}\color{tomato}{\left({\frac{2*2}{3}}\right)^3+\left({\frac{7*2}{3}}\right)^3\mathbf{\color{blue}{\;=\;}}\left({\frac{2}{3}}\right)^3+\left({\frac{7}{3}}\right)^3\mathbf{\color{blue}{\;=\;}}{\frac{104}{8}}\mathbf{\color{blue}{\;=\;}}13}\end{align}\)

(Integral Sum of Two Rational Cubes) (OEIS A020898) (OEIS A228499)

\((x^3+y^3)/z^3=n~\to~\) [x waarde] (OEIS A190356)  [y waarde] (OEIS A190580)  [z waarde] (OEIS A190581)

Kleinste positieve oplossingen \(~\to~\) [x waarde] (OEIS A254326)  [y waarde] (OEIS A254324)

104.13
Schakelaar
\(\mathbf[0\gets\to1000\mathbf]\)
“Allemaal Getallen”

\(\Huge\bbox[border:0]{⏮}\)

\(\Huge\bbox[border:0]{⯬}\)

\(\Huge\bbox[border:0]{⏴}\)

\(\Huge\bbox[border:0]{⏵}\)

\(\Huge\bbox[border:0]{⯮}\)

\(\Huge\bbox[border:0]{⏭}\)

\(104\)\(2^3*13\)\(8\)\(210\)
\(1,2,4,8,13,26,52,104\)
\(1101000_2\)\(150_8\)\(68_{16}\)
   

Uit de collectie 'Allemaal Getallen' van Ir. Jos Heynderickx
Toevoegingen & Bewerking & Layout door Patrick De Geest (email)
Laatste update 10 augustus 2024