How to show that $(a/b)^2$ in this situation cannot be an integer
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
103784
Show that $n^2+11n+2$ is not divisible by $113^2$ ( n is integer)
64896
Dealing with non-integral powers on negative numbers
41872
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
11069
Deciding whether $2^{\sqrt2}$ is irrational/transcendental
86015
$\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
113168
If $a > b$, is $a^2 > b^2$?
125267
Prove that $2^{1/2}$ is irrational
139466
How to test if a double is an integer
115460
Proving $a\mid b^2,\,b^2\mid a^3,\,a^3\mid b^4,\ldots\implies a=b$ - why is my approach incorrect
82485
Show that the set of non zero rationals is not a cyclic group under multiplication.
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
71110
Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
76032
Prove that if m is a square integer then m is neither congruent to 2 modulo 5 nor congruent to 3 modulo 5
34666
Prove that the expression cannot be a power of 2
119582
How to select the right modulus to prove that there do not exist integers $a$ and $b$ such that $a^2+b^2=1234567$?