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On the diophantine equation x2 + 52k = yn

Muriefah F.

Demonstratio Mathematica

2006

Vol. 39, nr 2

285-289

In this paper we prove that the title equation where k >0 and n > 3, may have a solution in integers (x, y, k, n) only if 5\x and p \ k where p any odd prime dividing n, by using a recent result of Bilu, Hanrot and Voutier [3].

On Lucas pseudoprimes with a prescribed value of the Jacobi symbol

Rotkiewicz A., Schinzel A.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 1

77-80

Given integers P, Q with D = P^2 - 4Q [is not equal to] 0, -Q, -2Q, -3Q and [epsilon] = [...]1 every arithmetic progression ax + b, where (a, b) = 1 which contains an odd integer n[sub 0] with (D/n[sub 0]) = [epsilon] contains infinitely many strong Lucas pseudoprimes n with parameters P and Q such that (D/n) = [epsilon]. This theorem gives an affirmative answer to a question of C. Pomerance.