The Polynomial Sieve and Equal Sums of Like Polynomials
نویسندگان
چکیده
منابع مشابه
The Polynomial Sieve and Equal Sums of like Polynomials
A new “polynomial sieve” is presented and used to show that almost all integers have at most one representation as a sum of two values of a given polynomial of degree at least 3.
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Let f ∈ Z[x] be a polynomial of degree d. We establish the paucity of non-trivial positive integer solutions to the equation f(x1) + f(x2) = f(x3) + f(x4), provided that d ≥ 7. We also investigate the corresponding situation for equal sums of three like polynomials. Mathematics Subject Classification (2000): 11D45 (11P05)
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2014
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnt350