query: Demonstrate that there are no perfect squares ending with $8$
positive_passages.docid: 150446
positive_passages.text: Quadratic Modular Arithmetic
negative_passages.docid: 50615
negative_passages.text: Expressing a Non Negative Integer as Sums of Two Squares
negative_passages.docid: 44790
negative_passages.text: Find $n$ for which $\frac{n(n+1)}{2}$ is perfect square
negative_passages.docid: 72389
negative_passages.text: Positive integer $n$ such that $2n+1$ , $3n+1$ are both perfect squares
negative_passages.docid: 140433
negative_passages.text: The number of ways of writing an integer as a sum of two squares
negative_passages.docid: 33735
negative_passages.text: The square of an integer is congruent to 0 or 1 mod 4
negative_passages.docid: 154082
negative_passages.text: Product of factorials divided by factorial to produce perfect square
negative_passages.docid: 44182
negative_passages.text: Proving that an integer is even if and only if it is not odd
negative_passages.docid: 66216
negative_passages.text: Squares, Cubes and Prime numbers
negative_passages.docid: 41641
negative_passages.text: $(n-7)(n+7)=$ some perfect square
negative_passages.docid: 98440
negative_passages.text: Show that any non-negative rational integer may be written as the sum of two squares if it is of the form....
negative_passages.docid: 131625
negative_passages.text: Expressing an integer as the sum of three squares
negative_passages.docid: 112644
negative_passages.text: The product of two numbers that can be written as the sum of two squares
negative_passages.docid: 67161
negative_passages.text: No maximum(minimum) of rationals whose square is lesser(greater) than $2$.
negative_passages.docid: 127100
negative_passages.text: Countable or uncountable set 8 signs
negative_passages.docid: 131731
negative_passages.text: Primes that can't be written as sum of two squares. Mod
negative_passages.docid: 63774
negative_passages.text: If a and b are odd integers, then $8\mid (a^2-b^2)$