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On pairs of triangular numbers whose product is a perfect square and pairs of intervals of successive integers with equal sums of squares
In 1778 Leonhard Euler characterized triangular numbers that are perfect squares. Obviously, the product of any two such numbers is a perfect square too. Yet, there are many other solutions, that is, pairs $(k,k')$ such that $k(k+1)k'(k'+1)$ is a perfect square. We give explicit formulas characteriz
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