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 A088719 Numbers that can be represented as a^7 + b^7, with 0 < a < b, in exactly one way. 7
 129, 2188, 2315, 16385, 16512, 18571, 78126, 78253, 80312, 94509, 279937, 280064, 282123, 296320, 358061, 823544, 823671, 825730, 839927, 901668, 1103479, 2097153, 2097280, 2099339, 2113536, 2175277, 2377088, 2920695 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=1..28. 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 Cf. A003369, A155468 (8th powers). Sequence in context: A240417 A353940 A351270 * A321563 A034681 A351302 Adjacent sequences: A088716 A088717 A088718 * A088720 A088721 A088722 KEYWORD nonn AUTHOR Cino Hilliard, Nov 22 2003 EXTENSIONS Edited by Don Reble, May 03 2006 STATUS approved

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Last modified June 3 04:09 EDT 2023. Contains 363103 sequences. (Running on oeis4.)