Prove that no integer in the sequence $11,111,1111....... $ is a perfect square.
45911
Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer
78593
Prove that the product of four consecutive positive integers plus one is a perfect square
83862
How to prove that the number $1!+2!+3!+...+n!$ is never square?
77816
Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.
42289
prove that there are infinitely many numbers of the form $x = 111....1$ such that $31\mid x$
99606
Prove or disprove there exists a set of four numbers out of the $48$ positive integers of which product is a perfect square
104494
$m$ doesn't come in the sequence $a_n=[n+\sqrt{n}+\frac{1}{2}]$ iff m is a perfect square
81267
A simple doubt in number theory problem.
107448
proving that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$
63182
For every $n \ge 1$ there exist uniquely determined integers $a \gt 0$ and $b \gt 0$ such that $n = a^2b$ where $b$ is square-free.
155784
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
58171
Two problems about Squarefree numbers
22800
Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
24601
Proving that a natural number made entirely of 6's and 0's is not a square.
126494
Prove that there doesn't exist any integer $x \ge 3$ such that $x^2-1$ is prime.
19588
$n!+1$ being a perfect square
140405
Show that there does not exist any $n$ for which $a^n=a$ forall $a\in \Bbb Z_m$ where $m$ is divisible by the square of some prime.