query: Prove that the area of a Pythagoras triple is divisible by 2, 3 and then 6
positive_passages.docid: 26857
positive_passages.text: In any Pythagorean triplet at least one of them is divisible by $2$, $3$ and $5$.
negative_passages.docid: 16176
negative_passages.text: Primitive Pythagorean triple divisible by 3
negative_passages.docid: 89838
negative_passages.text: Prove that $3 \le a+b+c \le 2\sqrt{3}$ in a triangle
negative_passages.docid: 46158
negative_passages.text: A positive integer is divisible by $3$ iff 3 divides the sum of its digits
negative_passages.docid: 146851
negative_passages.text: Prove that $-3$ is a quadratic residue mod an odd prime $>3$ if and only if $p$ is of the form of $6n+1$
negative_passages.docid: 157884
negative_passages.text: For any prime $p>3$ show that 3 divides $2p^2+1$
negative_passages.docid: 4077
negative_passages.text: Using induction prove $n^3-n$ is divisible by 3 whenever n is a positive number.
negative_passages.docid: 52930
negative_passages.text: Prove or disprove : $a^3\mid b^2 \Rightarrow a\mid b$
negative_passages.docid: 147403
negative_passages.text: Formulas for calculating pythagorean triples
negative_passages.docid: 40565
negative_passages.text: How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
negative_passages.docid: 15348
negative_passages.text: prime divisor of $3n+2$ proof
negative_passages.docid: 38904
negative_passages.text: Prove that $(a + b + c)^{13}$ is divisible by $abc$ if $b|a^3$, $c|b^3$ and $a|c^3$.
negative_passages.docid: 8366
negative_passages.text: Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
negative_passages.docid: 5257
negative_passages.text: Proving that $(3n)!$ is divisible by $n! \times (n + 1)! \times (n + 2)!$ if $n$ is greater than 2
negative_passages.docid: 77383
negative_passages.text: Prove that $n^3=n \text{ mod }6$ for every integer $n$.
negative_passages.docid: 65430
negative_passages.text: Using the Well Ordering Principle to Show that n^3 - n is divisible by 6.
negative_passages.docid: 111267
negative_passages.text: Prove that: $2^a+3^b<3a+4b$