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
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.
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
KEYWORD
nonn
AUTHOR
Geoffrey Caveney, Jul 31 2023
STATUS
approved