Diophantine m-tuples for primes
نویسندگان
چکیده
In this paper, we show that if p is a prime and ifA = {a1, a2, . . . , am} is a set of positive integers with the property that aiaj +p is a perfect square for all 1 ≤ i < j ≤ m, then m < 3 · 2168. More generally, when p is replaced by a squarefree integer n, the inequality m ≤ f(ω(n)) holds with some function f , where ω(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.
منابع مشابه
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تاریخ انتشار 2005