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A364654
Numbers which are the sum or difference of two seventh powers.
0
0, 1, 2, 127, 128, 129, 256, 2059, 2186, 2187, 2188, 2315, 4374, 14197, 16256, 16383, 16384, 16385, 16512, 18571, 32768, 61741, 75938, 77997, 78124, 78125, 78126, 78253, 80312, 94509, 156250, 201811, 263552, 277749, 279808, 279935, 279936, 279937, 280064, 282123, 296320
OFFSET
1,3
COMMENTS
Don Zagier's conjecture that the polynomial x^7 + 3y^7 is injective on rational numbers is equivalent to the non-existence of any term in this sequence that is exactly 3 times another term in this sequence.
LINKS
Bjorn Poonen, Multivariable polynomial injections on rational numbers, arXiv:0902.3961 [math.NT], 2009-2010; Acta Arith. 145 (2010), no. 2, 123-127.
EXAMPLE
2059 = 3^7 - 2^7, 2315 = 3^7 + 2^7, 358061 = 6^7 + 5^7, 543607 = 7^7 - 6^7.
PROG
(PARI) T=thueinit('z^7+1);
is(n) = (n==0) || (#thue(T, n)>0); \\ Michel Marcus, Aug 01 2023
CROSSREFS
Sequence in context: A157070 A064070 A266993 * A139904 A167414 A065381
KEYWORD
nonn
AUTHOR
Geoffrey Caveney, Jul 31 2023
STATUS
approved