On the Diophantine equation $$X^{2N}+2^{2alpha }5^{2beta }{p}^{2gamma } = Z^5$$ |
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| Authors: | Eva G. Goedhart Helen G. Grundman |
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| Affiliation: | 1.Department of Mathematical Sciences,Lebanon Valley College,Annville,USA;2.Department of Mathematics,Bryn Mawr College,Bryn Mawr,USA |
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| Abstract: | We prove that for each prime p, positive integer (alpha ), and non-negative integers (beta ) and (gamma ), the Diophantine equation (X^{2N} + 2^{2alpha }5^{2beta }{p}^{2gamma } = Z^5) has no solution with N, X, (Zin mathbb {Z}^+), (N > 1), and (gcd (X,Z) = 1). |
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