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Results tagged with diophantine-equations
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user 61879
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 many Pythagorean triples are there in which every member is triangular?
I tried the following which hasn't yet returned a solution:
Suppose we want to find a Pythagorean triple $(a,b,c)$ such that $b-a=1$. Then we can parameterize such solutions by,
$\bigl (\frac{x-1}{2 …
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