@fonfox and George: I will just point out that there already is a tag name (
square-numbers). I am not sure whether it was necessary to create a new tag, but maybe (perfect-squares) and (square-numbers) could be synonyms. See also
here. —
Martin Sleziak 10 secs ago
I tried working out a solution to satisfy this equation and I got that this has no solution, however:
$$1^2 + 2^2 + 2^2 = 3^2$$
so it does have a solution.
I started off with the equation:
$$a^2 + b^2 + c^2 = d^2$$
Therefore $a^2 + b^2 = d^2 - c^2$ and therefore:
$$(a + b)^2 - 2ab = (d + c)...
The question is quite general and looks to explore the properties of quotient rings of the form $$\mathbb{Z}_{m}[X] / (f(x)) \quad \text{and} \quad \mathbb{R}[X]/(f(x))$$
where $m \in \mathbb{N}$
Classic examples of how one can treat such rings is to find relationships like $$\mathbb{Z}[x]/(1-...
