\(58=13+14+15+16\) (som van opeenvolgende gehele getallen)

\(58=28+30\) (som van opeenvolgende pare getallen)

\(58=2+3+5+7+11+13+17\) (som van opeenvolgende priemgetallen)

\(58=((0;0;3;7)\,(1;2;2;7)\,(1;4;4;5)\,(2;2;5;5)\,(2;3;3;6))\lower2pt{\Large{\color{teal}{➋}}}\to\{\#5\}\)

\(58 \mathbf{\color{blue}{\;=\;}}1^3+1^3+1^3+1^3+3^3+3^3\mathbf{\color{blue}{\;=\;}}1^3+1^3+2^3+2^3+2^3+2^3+2^3+2^3+2^3\mathbf{\color{blue}{\;=\;}}\)

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

\(58=2*29\) en de som van de cijfers van \(58\) is gelijk aan de som van de cijfers van de priemfactoren \(2\) en \(29\) :

\(\qquad\;\,5+8\mathbf{\color{blue}{\;=\;}}2+2+9\mathbf{\color{blue}{\;=\;}}13\)

\(58\mathbf{\color{blue}{\;=\;}}3^2+7^2~~\) (enige oplossing met limieten grondtal \(9999\) en exponent \(19\) )

58.1

\(58\mathbf{\color{blue}{\;=\;}}\)(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 \(m=6~~(+4)\).

\(58\mathbf{\color{blue}{\;=\;}}\)(som van vier derdemachten)

\(\qquad\;\,(z\gt1000)\)

\(\qquad\;\,\bbox[3px,border:1px solid]{1^3+1^3+(-2)^3+4^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-5)^3+10^3+16^3+(-17)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{1^3+25^3+34^3+(-38)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-17)^3+22^3+43^3+(-44)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{4^3+43^3+58^3+(-65)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-47)^3+(-47)^3+(-89)^3+97^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-89)^3+100^3+115^3+(-122)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-62)^3+(-113)^3+(-173)^3+190^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{1^3+(-95)^3+(-185)^3+193^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-35)^3+(-161)^3+(-173)^3+211^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{4^3+55^3+235^3+(-236)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-95)^3+121^3+274^3+(-278)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{16^3+61^3+277^3+(-278)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-155)^3+190^3+277^3+(-290)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-5)^3+64^3+295^3+(-296)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{49^3+175^3+277^3+(-299)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-131)^3+136^3+298^3+(-299)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-41)^3+(-206)^3+(-272)^3+307^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{88^3+235^3+280^3+(-329)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-23)^3+(-194)^3+(-314)^3+337^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-68)^3+247^3+292^3+(-341)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-152)^3+247^3+304^3+(-341)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{100^3+151^3+331^3+(-344)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{1^3+76^3+382^3+(-383)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{172^3+277^3+328^3+(-395)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{106^3+(-209)^3+(-386)^3+403^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{67^3+(-263)^3+(-377)^3+415^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-77)^3+(-83)^3+(-413)^3+415^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-5)^3+(-161)^3+(-413)^3+421^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{250^3+277^3+445^3+(-500)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{184^3+382^3+421^3+(-515)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{280^3+(-329)^3+(-509)^3+526^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-104)^3+337^3+478^3+(-527)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{172^3+232^3+505^3+(-527)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-8)^3+268^3+529^3+(-551)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-131)^3+430^3+466^3+(-563)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-392)^3+445^3+532^3+(-563)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{1^3+190^3+568^3+(-575)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{4^3+205^3+637^3+(-644)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{193^3+(-293)^3+(-647)^3+661^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{208^3+337^3+634^3+(-671)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-311)^3+505^3+592^3+(-674)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{151^3+334^3+646^3+(-677)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-80)^3+403^3+640^3+(-689)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-272)^3+319^3+763^3+(-770)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{85^3+100^3+733^3+(-734)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-251)^3+(-251)^3+(-716)^3+736^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-347)^3+352^3+781^3+(-782)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{295^3+(-521)^3+(-719)^3+787^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-710)^3+736^3+775^3+(-797)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-221)^3+(-542)^3+(-698)^3+799^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-290)^3+(-524)^3+(-707)^3+805^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{268^3+583^3+691^3+(-818)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{22^3+(-629)^3+(-689)^3+832^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{1^3+(-161)^3+(-833)^3+835^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-143)^3+466^3+793^3+(-842)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-59)^3+136^3+877^3+(-878)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-179)^3+508^3+844^3+(-899)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{475^3+(-740)^3+(-761)^3+904^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{295^3+(-374)^3+(-893)^3+904^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-341)^3+703^3+778^3+(-920)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-134)^3+547^3+862^3+(-929)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-275)^3+529^3+877^3+(-929)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{(-149)^3+247^3+988^3+(-992)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{1^3+361^3+982^3+(-998)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{190^3+625^3+913^3+(-1004)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{427^3+(-656)^3+(-944)^3+1015^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{415^3+(-635)^3+(-965)^3+1027^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{277^3+493^3+988^3+(-1034)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,\bbox[3px,border:1px green solid]{436^3+(-914)^3+(-983)^3+1177^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad\;\,(z\gt1000)\)

\(58\mathbf{\color{blue}{\;=\;}}\)(som van vijf vijfdemachten)

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

58.2

\(58^2\mathbf{\color{blue}{\;=\;}}29^3-145^2\mathbf{\color{blue}{\;=\;}}40^2+42^2\mathbf{\color{blue}{\;=\;}}842^2-840^2\)

\(58^3\mathbf{\color{blue}{\;=\;}}154^2+414^2\mathbf{\color{blue}{\;=\;}}174^2+406^2\mathbf{\color{blue}{\;=\;}}899^2-783^2\mathbf{\color{blue}{\;=\;}}\bbox[2px,border:1px brown dashed]{1711^2-1653^2}\)

58.3

\(58^4=11316496\enspace\) en \(\enspace1+1+31+6+4+9+6=58\)

\(58^7=2207984167552\enspace\) en \(\enspace2+2+0+7+9+8+4+1+6+7+5+5+2=58\)

58.4
In een periode van \(400\) jaar valt nieuwjaarsdag \(58\) maal op zondag, dinsdag of vrijdag (zie ook bij en ) 58.5
Met de cijfers van \(0\) tot \(9\) kan men \(58\) schrijven als \(58=5+{\Large{36\over4}}+{\Large{70\over2}}+{\Large{81\over9}}\) 58.6
Er zijn twee rechthoekige driehoeken met gehele zijden en waarvan één zijde \(58\) is : \((40;42;58),(58;840;842)\) 58.7
\(58\) als resultaat met breuken waarin de cijfers van \(1\) tot \(9\) exact één keer voorkomen : (\(geen\) oplossingen) :
\(58\) als resultaat met breuken waarin de cijfers van \(0\) tot \(9\) exact één keer voorkomen : (\(3\) oplossingen) :
\(358092/6174=453096/7812=458316/7902=58\) 		58.8
Men moet \(58\) tot minimaal de \(2450\)ste macht verheffen opdat in de decimale expansie exact \(58\) \(58\)'s verschijnen.
Terloops : \(58\)\(^{2450}\) heeft een lengte van \(4321\) cijfers. 		58.9
\(58\) als som van twee priemgetallen die bovendien allemaal oneven zijn :

$$ 2\;odd\;primes \left[ \begin{matrix} &5&+&53\\ &11&+&47\\ &17&+&41\\ &29&+&29 \end{matrix} \right. $$

\(58\) als som van drie priemgetallen die bovendien allemaal verschillend zijn :

$$ 3\;dif\!ferent\;primes \left[ \begin{matrix} &\mathbf{2}&+&\mathbf{3}&+&\mathbf{53}\\ &\mathbf{2}&+&\mathbf{13}&+&\mathbf{43}\\ &\mathbf{2}&+&\mathbf{19}&+&\mathbf{37} \end{matrix} \right. $$

58.10

\(58^2=3364=(-3-3+64)^3\)

58.11

\(58\) is het kleinste Smith getal met een priemgetal als cijfersom. Een Smith getal is een samengesteld getal waarbij zijn

cijfersom gelijk is aan de cijfersom van zijn priemfactoren: \(5+8\mathbf{\color{blue}{\;=\;}}2+(2+9)\mathbf{\color{blue}{\;=\;}}13\). (OEIS A006753)

58.12
\(58\) kan niet geschreven worden als verschil van twee machten \(x^m\) en \(y^n\) waarbij \(x~\&~y\gt1\) en \(m~\&~n\gt1\).
Vermoedelijk volledige lijst betreffende het verschil van twee machten → (OEIS A074981) 		58.13

\(5\)\(^{58}\)\(~=~34694469519536141888238489627838134765625\) is de hoogst gekende macht van \(5\) waarbij geen cijfer \(0\)

voorkomt in de decimale expansie. (Zeroless powers) (OEIS A008839)

58.14

Som der reciproken van partitiegetallen van \(58\) is \(1\) op dertien wijzen

Er zijn geen partities met unieke termen.

\((1)~~58=3+3+4+24+24~~\) en \(~~1={\Large\frac{1}{3}}+{\Large\frac{1}{3}}+{\Large\frac{1}{4}}+{\Large\frac{1}{24}}+{\Large\frac{1}{24}}\)

\((2)~~58=2+6+10+10+15+15~~\) en \(~~1={\Large\frac{1}{2}}+{\Large\frac{1}{6}}+{\Large\frac{1}{10}}+{\Large\frac{1}{10}}+{\Large\frac{1}{15}}+{\Large\frac{1}{15}}\)

\((3)~~58=2+7+7+14+14+14~~\) en \(~~1={\Large\frac{1}{2}}+{\Large\frac{1}{7}}+{\Large\frac{1}{7}}+{\Large\frac{1}{14}}+{\Large\frac{1}{14}}+{\Large\frac{1}{14}}\)

\((4)~~58=2+8+8+8+16+16~~\) en \(~~1={\Large\frac{1}{2}}+{\Large\frac{1}{8}}+{\Large\frac{1}{8}}+{\Large\frac{1}{8}}+{\Large\frac{1}{16}}+{\Large\frac{1}{16}}\)

\((5)~~58=2+8+8+10+10+20~~\) en \(~~1={\Large\frac{1}{2}}+{\Large\frac{1}{8}}+{\Large\frac{1}{8}}+{\Large\frac{1}{10}}+{\Large\frac{1}{10}}+{\Large\frac{1}{20}}\)

\((6)~~58=3+3+8+12+16+16~~\) en \(~~1={\Large\frac{1}{3}}+{\Large\frac{1}{3}}+{\Large\frac{1}{8}}+{\Large\frac{1}{12}}+{\Large\frac{1}{16}}+{\Large\frac{1}{16}}\)

\((7)~~58=3+3+9+10+15+18~~\) en \(~~1={\Large\frac{1}{3}}+{\Large\frac{1}{3}}+{\Large\frac{1}{9}}+{\Large\frac{1}{10}}+{\Large\frac{1}{15}}+{\Large\frac{1}{18}}\)

\((8)~~58=3+3+10+10+12+20~~\) en \(~~1={\Large\frac{1}{3}}+{\Large\frac{1}{3}}+{\Large\frac{1}{10}}+{\Large\frac{1}{10}}+{\Large\frac{1}{12}}+{\Large\frac{1}{20}}\)

\((9)~~58=4+4+5+5+20+20~~\) en \(~~1={\Large\frac{1}{4}}+{\Large\frac{1}{4}}+{\Large\frac{1}{5}}+{\Large\frac{1}{5}}+{\Large\frac{1}{20}}+{\Large\frac{1}{20}}\)

\((10)~~58=3+8+8+9+9+9+12~~\) en \(~~1={\Large\frac{1}{3}}+{\Large\frac{1}{8}}+{\Large\frac{1}{8}}+{\Large\frac{1}{9}}+{\Large\frac{1}{9}}+{\Large\frac{1}{9}}+{\Large\frac{1}{12}}\)

\((11)~~58=4+4+10+10+10+10+10~~\) en \(~~1={\Large\frac{1}{4}}+{\Large\frac{1}{4}}+{\Large\frac{1}{10}}+{\Large\frac{1}{10}}+{\Large\frac{1}{10}}+{\Large\frac{1}{10}}+{\Large\frac{1}{10}}~~~~\)

\((12)~~58=4+6+6+6+12+12+12~~\) en \(~~1={\Large\frac{1}{4}}+{\Large\frac{1}{6}}+{\Large\frac{1}{6}}+{\Large\frac{1}{6}}+{\Large\frac{1}{12}}+{\Large\frac{1}{12}}+{\Large\frac{1}{12}}\)

\((13)~~58=5+5+5+8+8+12+15~~\) en \(~~1={\Large\frac{1}{5}}+{\Large\frac{1}{5}}+{\Large\frac{1}{5}}+{\Large\frac{1}{8}}+{\Large\frac{1}{8}}+{\Large\frac{1}{12}}+{\Large\frac{1}{15}}\)

(OEIS A125726)

58.15

\(\begin{align}58\mathbf{\color{blue}{\;=\;}}\left({\frac{28747}{7083}}\right)^3-\left({\frac{14653}{7083}}\right)^3\mathbf{\color{blue}{\;=\;}}\left({\frac{502035605557831043}{190549594455179400}}\right)^3+\left({\frac{650099621818168957}{190549594455179400}}\right)^3\end{align}\)

(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)

58.16

\(58\)\(^{1}\)\(+58\)\(^{3}\)\(+58\)\(^{4}\)\(+58\)\(^{7}\)\(+58\)\(^{6}\)\(+58\)\(^{4}\)\(+58\)\(^{5}\)\(+58\)\(^{0}\)\(+58\)\(^{7}\)\(+58\)\(^{5}\)\(+58\)\(^{3}\)\(+58\)\(^{7}\)\(+58\)\(^{6}\)\(+58\)\(^{8}\)\(+58\)\(^{3}\)\(\mathbf{\color{blue}{\;=\;}}134764507537683~~\)
(OEIS A236067)

58.17
Schakelaar
\(\mathbf[0\gets\to1000\mathbf]\)
“Allemaal Getallen”

\(\Huge\bbox[border:0]{⏮}\)

\(\Huge\bbox[border:0]{⯬}\)

\(\Huge\bbox[border:0]{⏴}\)

\(\Huge\bbox[border:0]{⏵}\)

\(\Huge\bbox[border:0]{⯮}\)

\(\Huge\bbox[border:0]{⏭}\)

\(58\)\(2*29\)\(4\)\(90\)
\(1,2,29,58\)
\(111010_2\)\(72_8\)\(3\)A\(_{16}\)
   

Uit de collectie 'Allemaal Getallen' van Ir. Jos Heynderickx
Toevoegingen & Bewerking & Layout door Patrick De Geest (email)
Laatste update 6 november 2024