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10:32 AM
A new tag was created. We already have and also .
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Q: Does the equation $a^2 + b^2 + c^2 = d^2$ have solutions if $(a, b, c, d) > 0$?

George N. MissailidisI 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)...

@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
In fact, when I look at the synonyms for square-numbers, there already is a suggestion for this synonym.
Sep 20 '15 at 11:40, by barto
@barto I suggested the synonym -> , see here
 
 
2 hours later…
1:02 PM
And also tag has been created recently.
14
Q: How to deal with polynomial quotient rings

MathmoThe 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-...

 

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