query: proof for test of a perfect square
positive_passages.docid: 142580
positive_passages.text: Prove that a perfect square is either a multiple of $4$ or of the form $4q+1$.
negative_passages.docid: 91101
negative_passages.text: Proving $\sqrt2$ is irrational
negative_passages.docid: 155784
negative_passages.text: If $\gcd(a, b) = 1$ and if $ab = x^2$, prove that $a, b$ must also be perfect squares; where $a,b,x$ are in the set of natural numbers
negative_passages.docid: 28218
negative_passages.text: Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
negative_passages.docid: 127566
negative_passages.text: $2AB$ is a perfect square and $A+B$ is not a perfect square
negative_passages.docid: 131636
negative_passages.text: Proof of Raabe's test
negative_passages.docid: 141496
negative_passages.text: Could someone make the proof into a hinted exercise?
negative_passages.docid: 101832
negative_passages.text: Proof that sum of first $n$ cubes is always a perfect square
negative_passages.docid: 84220
negative_passages.text: Questions on perfect squares
negative_passages.docid: 126074
negative_passages.text: Proof of the irrationality of $\sqrt{3}$ - logic question
negative_passages.docid: 24820
negative_passages.text: Prove that if $n$ is a perfect square, then either $n \equiv 1 \pmod 4$, or $n \equiv 0 \pmod 4$.
negative_passages.docid: 48787
negative_passages.text: A number is a perfect square if and only if it has odd number of positive divisors
negative_passages.docid: 130499
negative_passages.text: How can $p^{q+1}+q^{p+1}$ be a perfect square?
negative_passages.docid: 152754
negative_passages.text: When is the sum of divisors a perfect square?
negative_passages.docid: 77081
negative_passages.text: Proving square root of a square is the same as absolute value
negative_passages.docid: 121469
negative_passages.text: Proof of observations on natural numbers being expressed as differences of squares.
negative_passages.docid: 94019
negative_passages.text: Find all $p$'s such that $p^4 + p^3 + p^2 + p +1$ is a perfect square.