Diophantine m-tuples for primes (CROSBI ID 115333)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
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
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano