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Keywords:
Diophantine equation; exponential equation; primitive divisor theorem
Summary:
In this paper, we find all solutions of the Diophantine equation $x^2+2^\alpha 5^\beta 17^\gamma = y^n$ in positive integers $x,y\geq 1$, $\alpha ,\beta ,\gamma ,n\geq 3$ with $\gcd (x,y)=1$.
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