OFFSET
1,1
COMMENTS
Conjecture: no number can be expressed as such a sum in more than one way.
No solutions to the 7.2.2 (A^7 + B^7 = C^7 + D^7), 7.2.3, 7.2.4, or 7.2.5 equations are known. The smallest 7.2.6 equation is: 125^7 + 24^7 = 121^7 + 94^7 + 83^7 + 61^7 + 57^7 + 27^7 = 476841744674549. - Jonathan Vos Post, May 04 2006
REFERENCES
Sastry, S. and Rai, T. "On Equal Sums of Like Powers." Math. Student 16, 18-19, 1948.
LINKS
R. L. Ekl, Equal Sums of Four Seventh Powers, Math. Comput. 65, 1755-1756, 1996.
R. L. Ekl, New Results in Equal Sums of Like Powers, Math. Comput. 67, 1309-1315, 1998.
Eric Weisstein's World of Mathematics, Diophantine Equation: 7th Powers
EXAMPLE
129 = 1^7+2^7.
MATHEMATICA
lst={}; e=7; Do[Do[x=a^e; Do[y=b^e; If[x+y==n, AppendTo[lst, n]], {b, Floor[(n-x)^(1/e)], a+1, -1}], {a, Floor[n^(1/e)], 1, -1}], {n, 3*8!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 23 2009 *)
PROG
(PARI) powers2(m1, m2, p1) = { for(k=m1, m2, a=powers(k, p1); if(a==1, print1(k", ")) ); } powers(n, p) = { z1=0; z2=0; c=0; cr = floor(n^(1/p)+1); for(x=1, cr, for(y=x+1, cr, z1=x^p+y^p; if(z1 == n, c++); ); ); return(c) }
CROSSREFS
KEYWORD
nonn
AUTHOR
Cino Hilliard, Nov 22 2003
EXTENSIONS
Edited by Don Reble, May 03 2006
STATUS
approved