query: Show that $(x,y,z)$ is a primitive Pythagorean triple then either $x$ or $y$ is divisible by $3$.
positive_passages.docid: 16176
positive_passages.text: Primitive Pythagorean triple divisible by 3
negative_passages.docid: 27984
negative_passages.text: Square matrices satisfying certain relations must have dimension divisible by $3$
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: 94516
negative_passages.text: If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
negative_passages.docid: 86285
negative_passages.text: Given positive integers $ x , y$ and that $3x^2 + x = 4y^2 +y$ Prove that $x-y$ is a perfect square
negative_passages.docid: 127422
negative_passages.text: Problem on Linear Diophantine Equation over 3 variables
negative_passages.docid: 92692
negative_passages.text: Prove $3(x^2y+y^2z+z^2x)(xy^2+yz^2+zx^2)\ge xyz(x+y+z)^3$
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: 13904
negative_passages.text: $p = x^2 + xy + y^2$ if and only if $p \equiv 1 \text{ mod }3$?
negative_passages.docid: 41563
negative_passages.text: Prove that if the sum of digits of a number is divisible by 3, so is the number itself.
negative_passages.docid: 10635
negative_passages.text: diophantine equations $x^3-2y^3=1$
negative_passages.docid: 26857
negative_passages.text: In any Pythagorean triplet at least one of them is divisible by $2$, $3$ and $5$.
negative_passages.docid: 139935
negative_passages.text: Show that any set of 7 distinct integers includes two integers $x$ and $y$, such that either $x-y$ or $x+y$ is divisible by 10
negative_passages.docid: 91921
negative_passages.text: Divisibility of $n\cdot2^n+1$ by 3.
negative_passages.docid: 9302
negative_passages.text: Questions about Divisibility of $2^n$ by $3$
negative_passages.docid: 136586
negative_passages.text: Making $x+\frac1y$, $y+\frac1z$, and $z+\frac1x$ all integer.
negative_passages.docid: 43510
negative_passages.text: For what integer values of $y$ is $\frac{3y-1}{y-3}$ an integer?