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A088677
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Numbers that can be represented as a^6+b^6, with 0<a<b, in exactly one way.
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5
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65, 730, 793, 4097, 4160, 4825, 15626, 15689, 16354, 19721, 46657, 46720, 47385, 50752, 62281, 117650, 117713, 118378, 121745, 133274, 164305, 262145, 262208, 262873, 266240, 277769, 308800, 379793, 531442, 531505, 532170, 535537, 547066
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Conjecture: no number can be expressed such a sum in more than one way.
Ekl (1996) has searched and found no solutions to the 6.2.2 Diophantine equation A^6 + B^6 = C^6 + D^6 with sums less than 7.25 * 10^26. - Jonathan Vos Post (jvospost3(AT)gmail.com), May 04 2006
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REFERENCES
| Ekl, R. L. "New Results in Equal Sums of Like Powers." Math. Comput. 67, 1309-1315, 1998.
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LINKS
| Eric Weisstein's World of Mathematics, Diophantine Equation: 6th Powers.
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EXAMPLE
| 65 = 1^6+2^6.
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MATHEMATICA
| lst={}; e=6; 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, 2*8!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 22 2009]
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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) }
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CROSSREFS
| Cf. A003358.
Sequence in context: A020292 A031421 A200890 * A034680 A017675 A013954
Adjacent sequences: A088674 A088675 A088676 * A088678 A088679 A088680
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KEYWORD
| nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Nov 22 2003
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EXTENSIONS
| Edited by Don Reble (djr(AT)nk.ca), May 03 2006
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