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Diophantine m-tuples for primes (CROSBI ID 115333)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Dujella, Andrej ; Luca, Florian Diophantine m-tuples for primes // International mathematics research notices, 47 (2005), 2913-2940-x

Podaci o odgovornosti

Dujella, Andrej ; Luca, Florian

engleski

Diophantine m-tuples for primes

In this paper, we show that if p is a prime and if A=\a_1, a_2, ..., a_m\ is a set of positive integers with the property that a_ia_j+p is a perfect square for all 1 <= i < j <= m, then m < 3*2^{; ; ; ; 168}; ; ; ; . More generally, when p is replaced by a squarefree integer n, the inequality m <= f(omega(n)) holds with some function f, where omega(n) is the number of prime divisors of n. We also give upper bounds for m when p is replaced by an arbitrary integer which hold on a set of n of asymptotic density one.

Diophantine m-tuples; variable elimination; Ramsey numbers

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Podaci o izdanju

47

2005.

2913-2940-x

objavljeno

1073-7928

Povezanost rada

Matematika

Indeksiranost