query: If $n$ is an integer then $n^2$ is the same as $0$ or $1\pmod 4$?
positive_passages.docid: 33735
positive_passages.text: The square of an integer is congruent to 0 or 1 mod 4
negative_passages.docid: 100426
negative_passages.text: Let $a$ and $b$ be integers. Show that if $a \equiv b \pmod{p}$ for every prime $p$, then $a = b$.
negative_passages.docid: 10191
negative_passages.text: Binomial theorem: divisibility by $n^2$
negative_passages.docid: 152638
negative_passages.text: The set of integers $n$ expressible as $n=x^2+xy+y^2$
negative_passages.docid: 106380
negative_passages.text: What is $n!$ when $n=0$?
negative_passages.docid: 143357
negative_passages.text: Comparing $2^n$ to $n!$
negative_passages.docid: 68233
negative_passages.text: Fermat's little theorem's proof for a negative integer
negative_passages.docid: 76032
negative_passages.text: Prove that if m is a square integer then m is neither congruent to 2 modulo 5 nor congruent to 3 modulo 5
negative_passages.docid: 153123
negative_passages.text: Proving by induction $4^n  0$
negative_passages.docid: 38882
negative_passages.text: If $n$ is a positive integer such that $n^3 − n − 6 = 0$, then, for every positive integer $m$ with $m \not = n$, $m^3 − m − 6 \not = 0$.
negative_passages.docid: 34588
negative_passages.text: Number Theory: $p!+p=n^2$, $p$ = prime
negative_passages.docid: 33866
negative_passages.text: Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
negative_passages.docid: 112575
negative_passages.text: Finding integer solutions of $m^2-n^5 = m - n$
negative_passages.docid: 64782
negative_passages.text: How to prove if $n$ is prime and $n | a^2$ then $n | a$?
negative_passages.docid: 88036
negative_passages.text: Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$
negative_passages.docid: 140086
negative_passages.text: Does $3-4+1$ equal $0$ or $-2$.. or maybe $2$?
negative_passages.docid: 70386
negative_passages.text: Proof by induction: $2^n > n^2$ for all integer $n$ greater than $4$