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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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A problem on the finiteness of solutions to a Diophantine equations

Given two positive integers $a,b$, and an odd prime $p$, I want to know whether the number of solutions to the following equation is finite: $X^2=a+bp^{Y}$ where $X,Y$ are variables and are integers …
Tao Feng's user avatar