Prove that if m is an integer and there is a rational number r/s so that (r/s)^2 = m, then there is an integer n so that n^2 = m.
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
15191
If $a^2$ divides $b^2$, then $a$ divides $b$
31744
Proving that there is an irrational number between any two unequal rational numbers.
74713
Show that for any natural numbers, if $S(x)=S(y)$ then $x=y$.
156646
If $x$ is rational then $\,x+\frac{1}x \,$ is an integer $\iff x = \pm 1$
49427
$l^2+m^2=n^2$ $\implies$ $lm$ is always a multiple of 3 when $l,m,n,$ are positive integers.
60804
About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
35837
How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?
78287
Prove that if $n$ is not the square of a natural number, then $\sqrt{n}$ is irrational.
33786
Proof that a certain fraction is always an integer
152638
The set of integers $n$ expressible as $n=x^2+xy+y^2$
6582
Prove the existence of the square root of $2$.
9846
Prove $n-m \mid n^r - m^r\,$ [Factor Theorem, monomial case]
257
Prove that : $m_{a}m_{b}m_{c}\leq\frac{Rs^{2}}{2}$
153313
Prove that for all integers $ a $ and $ b $, if $ a $ divides $ b $, then $ a^{2} $ divides $ b^{2} $.
87764
Prove that the difference between two rational numbers is rational
142008
Find all natural numbers $n$ such that ${(n+1)}^{1/2}-{(n-1)}^{1/2}$ is rational