On Solutions of the Diophantine Equations p^3 + q^3 = z^2 and p^3 - q^3 = z^2 when p, q are Primes
نویسندگان
چکیده
منابع مشابه
The Diophantine Equation 8x + py = z2
Let p be a fixed odd prime. Using certain results of exponential Diophantine equations, we prove that (i) if p ≡ ± 3(mod 8), then the equation 8 (x) + p (y) = z (2) has no positive integer solutions (x, y, z); (ii) if p ≡ 7(mod 8), then the equation has only the solutions (p, x, y, z) = (2 (q) - 1, (1/3)(q + 2), 2, 2 (q) + 1), where q is an odd prime with q ≡ 1(mod 3); (iii) if p ≡ 1(mod 8)...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Mathematics
سال: 2018
ISSN: 2279-087X,2279-0888
DOI: 10.22457/apam.v18n1a7