Prove that if square root of ${m\over n}$ is rational, then $m$ and $n$ are both perfect squares
1190
Square Root of Rational Number $\frac{A}{B}$
136366
Show that if $2+2\sqrt{28n^2+1}$ is an integer then it must be perfect square.
86285
Given positive integers $ x , y$ and that $3x^2 + x = 4y^2 +y$ Prove that $x-y$ is a perfect square
56877
Show that $\sqrt{4 + 2\sqrt{3}} - \sqrt{3}$ is rational.
35052
Prove that if $m^2 + n^2$ is divisible by $4$, then both $m$ and $n$ are even numbers.
23712
$F$ is a finite field of size $s$. Prove that if $s=2^m$ for some $m>0$, then all elements of F have a square root.
2614
Prove that , any primitive root $r$ of $p^n$ is also a primitive root of $p$
53945
The square root of a prime number is irrational
21457
Prove $\sqrt{2\sqrt{3\sqrt{\cdots\sqrt{n}}}}<3$ by induction.
24820
Prove that if $n$ is a perfect square, then either $n \equiv 1 \pmod 4$, or $n \equiv 0 \pmod 4$.
9146
Proving that a list of perfect square numbers is complete
67356
When is $2^x+3^y$ a perfect square?
94019
Find all $p$'s such that $p^4 + p^3 + p^2 + p +1$ is a perfect square.
73277
Prove $[\sqrt{x}+\sqrt{x+1}]=[\sqrt{4x+2}], x \in \Bbb N$
104494
$m$ doesn't come in the sequence $a_n=[n+\sqrt{n}+\frac{1}{2}]$ iff m is a perfect square
126074
Proof of the irrationality of $\sqrt{3}$ - logic question
81778
If $m|n$ and $a$ is a primitive root of $n$, show that $a$ is a primitive root of $m$ (understanding a tip)