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On a Problem of Brocard 总被引:1,自引:0,他引:1
It is proved that, if P is a polynomial with integer coefficients,having degree 2, and 1 > > 0, then n(n 1) ...(n k + 1) = P(m) has only finitely many natural solutions(m,n,k), n k > n, provided that the abc conjecture is assumedto hold under Szpiro's formulation. 2000 Mathematics SubjectClassification 11D75, 11J25, 11N13. 相似文献
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Alexandru Gica 《Journal of Number Theory》2002,94(1):80-89
The aim of this paper is to show that for any n∈N, n>3, there exist a, b∈N* such that n=a+b, the “lengths” of a and b having the same parity (see the text for the definition of the “length” of a natural number). Also we will show that for any n∈N, n>2, n≠5, 10, there exist a, b∈N* such that n=a+b, the “lengths” of a and b having different parities. We will prove also that for any prime p≡7(mod 8) there exist a, b∈N* such that p=a2+b, the “length” of b being an even number. 相似文献
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