This thesis explores the factorization of odd integers that can be expressed in two different ways as $mx^2 \pm ny^2$. A special case, when $m = n = 1$, was the subject of study by Pierre de Fermat and Leonhard Euler, whose solutions we also present. We continue with a generalization of the problem and present another solution by Lucas and Mathews. As the negative case $mx^2 - ny^2$ turns out to be quite different from the positive case $mx^2 + ny^2$, we take a look at Pell’s equation $x^2 - mny^2 = 1$. We see that Pell-related solutions of the problem produce trivial factorizations.
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