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 Sep30 awarded Popular Question Aug9 awarded Popular Question Jul2 awarded Curious Jun5 answered 'Obvious' theorems that are actually false Jan21 accepted Is there any pythagorean triple (a,b,c) such that $a^2 \equiv 1 \bmod b^{2}$ Jul22 comment Is there any pythagorean triple (a,b,c) such that $a^2 \equiv 1 \bmod b^{2}$ awesome - thank you! Jul18 awarded Nice Question Jul16 comment Nature of a triangle with vertices $z_1, z_2$ and $-1$ such that $|z_1|=|z_2|=1=z_1+z_2$ |z1|=|z2|=1 means that z1 and z2 lie on the unit circle. z1+z2=1 means that the imaginary parts cancel out - i.e. z1 and z2 lie on a vertical line - so what do the real parts have to be? Jul16 comment How many real roots does $(x-a)^3+(x-b)^3+(x-c)^3$ have? yeap, that's the key, and all that is needed Jul16 awarded Teacher Jul15 comment Is there any pythagorean triple (a,b,c) such that $a^2 \equiv 1 \bmod b^{2}$ sweet, I did see the second equation but had no idea how to use it Jul15 answered Pigeonhole principle: show that a class of nine has at least five male or five female students. Jul15 asked Is there any pythagorean triple (a,b,c) such that $a^2 \equiv 1 \bmod b^{2}$ Jul15 awarded Yearling Jul15 accepted Find $m, n$ such that $\frac{n^2 + 1}{m^2 + 1 }$ is an integer multiple of a perfect square Jul14 comment Find $m, n$ such that $\frac{n^2 + 1}{m^2 + 1 }$ is an integer multiple of a perfect square (1) Sweet, that makes sense. (2) How did you go about finding (18,5)? Jul14 awarded Commentator Jul14 comment Find $m, n$ such that $\frac{n^2 + 1}{m^2 + 1 }$ is an integer multiple of a perfect square @CalvinLin thanks, that's nice for $d=5$, but right now I'm after $d=2$ and the actual theory/approach to this kind of a problem Jul14 asked Find $m, n$ such that $\frac{n^2 + 1}{m^2 + 1 }$ is an integer multiple of a perfect square Jan11 accepted Show $15x^{2} - 7y^{2} = 9$ has no integer solutions