Abstract
Let a, b, c, r be positive integers such that a 2 + b 2 = c r, min(a, b, c, r) > 1, gcd(a, b) = 1, a is even and r is odd. In this paper we prove that if b ≡ 3 (mod 4) and either b or c is an odd prime power, then the equation x 2 + b y = c z has only the positive integer solution (x, y, z) = (a, 2, r) with min(y, z) > 1.
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Le, M. A note on the diophantine equation x 2 + b y = c z . Czech Math J 56, 1109–1116 (2006). https://doi.org/10.1007/s10587-006-0082-9
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DOI: https://doi.org/10.1007/s10587-006-0082-9