Equal sums of two kth powors

[摘要] Let k greater than or equal to 5 be an integer, and let x greater than or equal to 1 be an arbitrary real number. We derive a bound O-epsilon,O-k(x(2/3k+epsilon) + x(3/krootk+2/k(k-1)+epsilon)), for the number of positive integers less than or equal to x which can be represented as a sum of two non-negative coprime kth powers, in essentially more than one way. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-10-01

[关键词] equal sums;like powers;rational points;upper bound