how to prove that $n(n+1)$ can't be square?
36011
Show that the product of two consecutive natural numbers is never a square.
47471
The square of n+1-th prime is less than the product of the first n primes.
23830
Proof that if $p\equiv3\,\left(\mbox{mod 4}\right)$ then $p$ can't be written as a sum of two squares
18932
Squares in arithmetic progression
92106
Prove that $n$ is a sum of two squares?
78287
Prove that if $n$ is not the square of a natural number, then $\sqrt{n}$ is irrational.
129351
Show that $\sqrt{n^2+1}-n$ converges to 0
50596
$p_1p_2...p_n +1$ is not square for $p_k = k$'th prime
140409
Prove that $\sqrt{n} > \ln n$
54355
$1+x+\ldots+x^n$ perfect square
52427
Prove, $\sqrt{n} \le (n!)^\frac{1}{n} \le \frac{n+1}{2} $
89175
Proof of $(a+b)^{n+1}$
107725
Prove that if $n$ is not divisible by $5$, then $n^4 \equiv 1 \pmod{5}$
35837
How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?
90102
How to prove that $p-1$ is squarefree infinitely often?
125702
There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$
22973
Show that an integer of the form $8k + 7$ cannot be written as the sum of three squares.