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Results tagged with diophantine-equations
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user 503012
Diophantine equations are polynomial equations $F=0$, or systems of polynomial equations $F_1=\ldots=F_k=0$, where $F,F_1,\ldots,F_k$ are polynomials in either $\mathbb{Z}[X_1,\ldots,X_n]$ of $\mathbb{Q}[X_1,\ldots,X_n]$ of which it is asked to find solutions over $\mathbb{Z}$ or $\mathbb{Q}$. Topics: Pell equations, quadratic forms, elliptic curves, abelian varieties, hyperelliptic curves, Thue equations, normic forms, K3 surfaces ...
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How can we solve the following number theory problem? [closed]
Let $m$ and $n$ be positive integers less than $2000$ which satisfies the equation $(m^2-mn-n^2)^2=1$. How can we determine the largest possible value of the expression $m^2+n^2$?