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2023 BIMC keystage3-IWYMIC individual Question 5

xIMC · 2023 BIMC keystage3-IWYMIC individual

Question 5

Consider the equation $10y^2-9x^{2022}=y^4$, where $x$ and $y$ are integers. If $m$ is the greatest possible value of $x+y$ and $n$ is the number of solutions $(x,y)$, what is $m+n$?