query: Pythagoras always divisible by 3
positive_passages.docid: 150528
positive_passages.text: Pythagorean triples $(a,b,c)$ and divisibility of $a$ or $b$ by $3$.
negative_passages.docid: 137608
negative_passages.text: Proof of Euclid's formula for primitive Pythagorean Triples
negative_passages.docid: 24053
negative_passages.text: How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
negative_passages.docid: 32653
negative_passages.text: Smallest integer divisible by all up to $n$
negative_passages.docid: 27984
negative_passages.text: Square matrices satisfying certain relations must have dimension divisible by $3$
negative_passages.docid: 153892
negative_passages.text: Number Theory divisibilty
negative_passages.docid: 1702
negative_passages.text: Proving that there are infinitely many primes with remainder of 2 when divided by 3
negative_passages.docid: 31074
negative_passages.text: Mathematical Induction divisibility $8\mid 3^{2n}-1$
negative_passages.docid: 132175
negative_passages.text: How many $5$-digit numbers with distinct digits are divisible by 3 (and generalize)
negative_passages.docid: 115264
negative_passages.text: Find when three numbers have the same remainder when divided by the same number
negative_passages.docid: 106847
negative_passages.text: Proof that $n^3+2n$ is divisible by $3$
negative_passages.docid: 96737
negative_passages.text: Geometric proof that a Pythagorean triple has a number divisible by $3$?
negative_passages.docid: 124816
negative_passages.text: Using the fact that $n^3 + 5n$ is divisible by $6$, infer that $n^4 - 2n^3 + 11n^2 + 14n$ is always divisible by $24$
negative_passages.docid: 15915
negative_passages.text: For any prime $p > 3$, why is $p^2-1$ always divisible by 24?
negative_passages.docid: 122207
negative_passages.text: Use the Division Algorithm to show the square of any integer is in the form $3k$ or $3k+1$
negative_passages.docid: 11470
negative_passages.text: Divisibility of integers
negative_passages.docid: 41295
negative_passages.text: Divisibility, LCM and GCD for fractions (rationals)