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number-theory share | cite | improve this question edited hours ago url silver badges bronze badges asked hours ago ellen ellen ellen ellen bronze badges $\endgroup$ $egingroup$ $y^ - x^ = $ is a pell equation $\endgroup$ – j. w. tanner hours ago $egingroup$ @almagest thank you, i am too trusting :)
pm $ then it is easy to check that $(m,n)=( m+ n, m+ n)$ is a solution to $y^ - x^ =\mp $. so given a solution $(m,n)$ to the original equation, $( m+ n, m+ n)$ is a larger solution. hence there are infinitely many. share | cite | improve this answer answered hours ago almagest almagest . k silver badges...
https://math.stackexchange.com/questions/3494364/prove-that-the-equation-has-infinitely-many-solutions-in-mathbbn2-x1
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