query: Proof that the sum of the even side and the hypotenuse of a coprime (and positive) Pythagorean triple is a square number
positive_passages.docid: 147403
positive_passages.text: Formulas for calculating pythagorean triples
negative_passages.docid: 60712
negative_passages.text: Induction Proof: Fibonacci Numbers Identity with Sum of Two Squares
negative_passages.docid: 34393
negative_passages.text: Variation of Pythagorean triplets: $x^2+y^2 = z^3$
negative_passages.docid: 126074
negative_passages.text: Proof of the irrationality of $\sqrt{3}$ - logic question
negative_passages.docid: 135458
negative_passages.text: When is a sum of consecutive squares equal to a square?
negative_passages.docid: 101832
negative_passages.text: Proof that sum of first $n$ cubes is always a perfect square
negative_passages.docid: 156564
negative_passages.text: Prove the identity $\sum_{{{\underset{k-even}{k=0}}}}^{n}{n \choose k}2^{k}=\frac{3^{n}+(-1)^{n}}{2}$
negative_passages.docid: 90904
negative_passages.text: Combinatorial proof of an identity with squared binomial coefficients
negative_passages.docid: 50615
negative_passages.text: Expressing a Non Negative Integer as Sums of Two Squares
negative_passages.docid: 57250
negative_passages.text: Proving that the sum and difference of two squares (not equal to zero) can't both be squares.
negative_passages.docid: 137175
negative_passages.text: Fermat's little theorem proof by Euler
negative_passages.docid: 23830
negative_passages.text: Proof that if $p\equiv3\,\left(\mbox{mod 4}\right)$ then $p$ can't be written as a sum of two squares
negative_passages.docid: 128575
negative_passages.text: Elementary proof that $3$ is a primitive root of a Fermat prime?
negative_passages.docid: 112644
negative_passages.text: The product of two numbers that can be written as the sum of two squares
negative_passages.docid: 12079
negative_passages.text: A positive polynomial is the sum of two squares in $\mathbb{R}[X]$
negative_passages.docid: 39021
negative_passages.text: Proving that $\sqrt{2}+\sqrt{3}$ is irrational
negative_passages.docid: 40952
negative_passages.text: Showing that sum of angles of hyperbolic triangle is strictly less than $\pi$