3 ADDITIVE CONGRUENCES TO A LARGE PRIME MODULUS

Authors
ATKINSON OD BRUDERN J COOK RJ
Citation
Od. Atkinson et al., 3 ADDITIVE CONGRUENCES TO A LARGE PRIME MODULUS, Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics, 55, 1993, pp. 355-368
Citations number
10
Categorie Soggetti
Mathematics, General","Statistic & Probability",Mathematics,"Statistic & Probability
Journal title
Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics → ACNP
ISSN journal
02636115
Volume
55
Year of publication
1993
Part
3
Pages
355 - 368
Database
ISI
SICI code
0263-6115(1993)55:<355:3ACTAL>2.0.ZU;2-N
Abstract
Let k greater-than-or-equal-to 3 and n > 6k be positive integers. The equations f(x) = a1x1k + ... + a(n)x(n)k = 0, g(x) = b1x1k + ... + b(n )x(n)k = 0, h(x) = c1x1k + ... + c(n)x(n)k = 0, with integer coefficie nts, have nontrivial p-adic solutions for all p > Ck8, where C is some positive constant. Further, for values k greater-than-or-equal-to K w e can take C = 1 + O(K-1/2).