A364654 Numbers which are the sum or difference of two seventh powers.

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

Author

Geoffrey Caveney, Jul 31 2023

Keywords

• nonn

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.

Examples

			2059 = 3^7 - 2^7, 2315 = 3^7 + 2^7, 358061 = 6^7 + 5^7, 543607 = 7^7 - 6^7.
		

Links

• Mathematics Stack Exchange, Are all bivariate polynomials of degree < 7 non-injective on rational numbers?
• Bjorn Poonen, Multivariable polynomial injections on rational numbers, arXiv:0902.3961 [math.NT], 2009-2010; Acta Arith. 145 (2010), no. 2, 123-127.

Crossrefs

Cf. A001015, A247099.

Programs

PARI

T=thueinit('z^7+1);
is(n) = (n==0) || (#thue(T, n)>0); \\ Michel Marcus, Aug 01 2023