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[ May 22, 2024 ] [ Last update December 29, 2024 ]
If you find a solution that is not present in this list of Sums of Five Fifthpowers Following is some Pari/GP code that automates the search for these sums of five fifthpowers. |
\\ This is my PARI/GP program code for WONplate 230 by PDG [May 23, 2024] → rnd5pow.gp f="D:/Teksten2024/Random-so5p.txt"; { scope=1500; print("Random between -",scope," and +",scope," limit up to 1000"); print(); write(f, "Random between -",scope," and +",scope," limit up to 1000"); write(f,); while(1==1, y=round(random(0.1)*scope*2-scope); x=round(random(0.1)*scope*2-scope); w=round(random(0.1)*scope*2-scope); v=round(random(0.1)*scope*2-scope); s4p=v^5+w^5+x^5+y^5; z=round(sqrtn(abs(s4p),5)); z=-1*sign(s4p)*z; n=s4p+z^5; if(v+w==0||v+x==0||v+y==0||v+z==0||w+x==0||w+y==0||w+z==0||x+y==0||x+z==0||y+z==0, n=99999); if(abs(n)<=1000, a=[v,w,x,y,z]; if(abs(a[1])>abs(a[2]),sw=a[1];a[1]=a[2];a[2]=sw); if(abs(a[2])>abs(a[3]),sw=a[2];a[2]=a[3];a[3]=sw); if(abs(a[3])>abs(a[4]),sw=a[3];a[3]=a[4];a[4]=sw); if(abs(a[4])>abs(a[5]),sw=a[4];a[4]=a[5];a[5]=sw); if(abs(a[1])>abs(a[2]),sw=a[1];a[1]=a[2];a[2]=sw); if(abs(a[2])>abs(a[3]),sw=a[2];a[2]=a[3];a[3]=sw); if(abs(a[3])>abs(a[4]),sw=a[3];a[3]=a[4];a[4]=sw); if(abs(a[1])>abs(a[2]),sw=a[1];a[1]=a[2];a[2]=sw); if(abs(a[2])>abs(a[3]),sw=a[2];a[2]=a[3];a[3]=sw); if(abs(a[1])>abs(a[2]),sw=a[1];a[1]=a[2];a[2]=sw); vv=a[1];ww=a[2];xx=a[3];yy=a[4];z=a[5]; print1(n," = "); if(vv<0, print1("(",vv,")"), print1(vv)); print1("^5+"); if(ww<0, print1("(",ww,")"), print1(ww)); print1("^5+"); if(xx<0, print1("(",xx,")"), print1(xx)); print1("^5+"); if(yy<0, print1("(",yy,")"), print1(yy)); print1("^5+"); if(z<0, print1("(",z,")"), print1(z)); print1("^5"); print; write1(f, n," = "); if(vv<0, write1(f, "(",vv,")"), write1(f, vv)); write1(f, "^5+"); if(ww<0, write1(f, "(",ww,")"), write1(f, ww)); write1(f, "^5+"); if(xx<0, write1(f, "(",xx,")"), write1(f, xx)); write1(f, "^5+"); if(yy<0, write1(f, "(",yy,")"), write1(f, yy)); write1(f, "^5+"); if(z<0, write1(f, "(",z,")"), write1(f, z)); write1(f, "^5"); write(f,); )); } \\ This is my PARI/GP program code for WONplate 230 by PDG [May 23, 2024] → so5p.gp \\ Instead of random picks this time all combinations from -b up to b are scanned, \\ for one particular value n. \\ But this comes with a price namely it runs for a very long time... f="D:/Teksten2024/Vijfdemachten666.txt"; { n=666 ; b=50; print("\e[38;5;92m",n," z<=",b,"\e[38;5;37m");print; write(f, n" z<="b);write(f,); for(y=-b,b, for(x=-b,b, for(w=-b,b, for(v=-b,b, fif=n-v^5-w^5-x^5-y^5; fiff=sqrtn(abs(fif),5); z=floor(fiff*sign(fif)); if(fiff==floor(fiff), \\ if(fiff==floor(fiff)&&v+w<>0&&v+x<>0&&v+y<>0&&v+z<>0&&w+x<>0&&w+y<>0&&w+z<>0&&x+y<>0&&x+z<>0&&y+z<>0, \\[ COPY THE BLUE SORTING/OUTPUT CODE FROM ABOVE HERE ] ))))); } print(Strchr(13)); |
Guidance to the world of OEIS sequences about at most 5 sums of fifth powers. (A236067) Fifth powers: a(n) = n^5. (A020896) Positive numbers k such that k = x^5 + y^5 has a solution in nonzero integers x,y. (A004842) Numbers that are the sum of at most 2 positive 5th powers. (A247099) Numbers which are the sum or difference of two fifth powers. {zero allowed} (A003348) Numbers that are the sum of 3 positive 5th powers. (A004843) Numbers that are the sum of at most 3 positive 5th powers. (A344641) Numbers that are the sum of three positive fifth powers in exactly one way. (A345010) Numbers that are the sum of three {positive} fifth powers in two or more ways. (A004844) Numbers that are the sum of at most 4 positive 5th powers. (A344642) Numbers that are the sum of four {positive} fifth powers in exactly one way. (A344645) Numbers that are the sum of four {positive} fifth powers in exactly two ways. (A345337) Numbers that are the sum of four {positive} fifth powers in three or more ways. (A003350) Numbers that are the sum of 5 positive 5th powers. (A004845) Numbers that are the sum of at most 5 positive 5th powers. (A342685) Numbers that are the sum of five {positive} fifth powers in two or more ways. (A342686) Numbers that are the sum of five {positive} fifth powers in exactly two ways. (A342687) Numbers that are the sum of five {positive} fifth powers in three or more ways. (A342688) Numbers that are the sum of five {positive} fifth powers in exactly three ways. (A344518) Numbers that are the sum of five {positive} fifth powers in four or more ways. (A344519) Numbers that are the sum of five {positive} fifth powers in exactly four ways. (A345863) Numbers that are the sum of five {positive} fifth powers in five or more ways. (A346257) Numbers that are the sum of five {positive} fifth powers in exactly five ways. (A345864) Numbers that are the sum of five {positive} fifth powers in six or more ways. (A133541) Sum of fifth powers of five consecutive primes. Sums of Five Fifthpowers [1..1000] Patrick De Geest Diophantine Equation--5th Powers from MathWorld A Table of Fifth Powers equal to Sums of Five Fifth Powers, 2009 by James Waldby Euler's sum of powers conjecture from Wikipedia Computing Minimal Equal Sums Of Like Powers | |||
A000230 Prime Curios! Prime Puzzle Wikipedia 230 Le nombre 230 |
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