query: Given that a is an integer, find possible $a$'s so that $2^{2a+1}+2^a+1$ is a perfect square
positive_passages.docid: 155363
positive_passages.text: Find all integers $(x, y)$ such that $1 + 2^x + 2^{2x + 1} = y^2$
negative_passages.docid: 157186
negative_passages.text: Finding integers satisfying $m^2 - n^2 = 1111$
negative_passages.docid: 107990
negative_passages.text: Does there exist an integer $x$ satisfying the following congruences?
negative_passages.docid: 81226
negative_passages.text: Find all integers $a$ for which $x^2-x+a$ divide $x^{13}+x+90$.
negative_passages.docid: 27427
negative_passages.text: Arranging numbers from $1$ to $n$ such that the sum of every two adjacent numbers is a perfect power
negative_passages.docid: 125702
negative_passages.text: There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$
negative_passages.docid: 112867
negative_passages.text: Find all digits $a,b$ such that the number $\overline{aabb}$ is a perfect square
negative_passages.docid: 21898
negative_passages.text: Find all primes $p$ such that $ p^3-4p+9 $ is a perfect square.
negative_passages.docid: 104920
negative_passages.text: Can we find positive integers $a$ and $k \geq 2$ with $2^n - 1 = a^k$?
negative_passages.docid: 105564
negative_passages.text: If $n$ is a positive integer greater than 1 such that $3n+1$ is perfect square, then show that $n+1$ is the sum of three perfect squares.
negative_passages.docid: 113511
negative_passages.text: What's a good algorithm to determine if an input is a perfect square?
negative_passages.docid: 131108
negative_passages.text: Can $3p^4-3p^2+1$ be square number?
negative_passages.docid: 44790
negative_passages.text: Find $n$ for which $\frac{n(n+1)}{2}$ is perfect square
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: 152643
negative_passages.text: $(xy + 1)(yz + 1)(zx + 1) $ is a perfect square if and only if each factor is
negative_passages.docid: 84283
negative_passages.text: If $a\neq 1$, find $(a+1)(a^2+1)(a^4+1)\ldots(a^{2^n}+1)$.
negative_passages.docid: 12967
negative_passages.text: Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer.