World!Of
Numbers

WON plate
|

[ May 22, 2024 ] [ Last update August 26, 2024 ]
Manually searching for Sums of Five Fifthpowers ⩽ 1000
By Patrick De Geest

∑ = 

5 + 

5 + 

5 + 

5 + 

5  

+/-   +/-   +/-   +/-   +/-
random   random   random   random   random
Randomize first four terms and adjust last one random scope

If you find a solution that is not present in this list of  Sums of Five Fifthpowers
please mail me the new find and will add it to the list.

Following is some Pari/GP code that automates the search for these sums of five fifthpowers.
Lowering the random scope value results in finding smaller solutions much sooner. Using
higher random scope values will make a find much rarer but more satisfying.


\\ 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));

A000230 Prime Curios! Prime Puzzle
Wikipedia 230 Le nombre 230














[ TOP OF PAGE]


( © All rights reserved )

Patrick De Geest - Belgium - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com