Showing there is no triplet of positive integers $(a,b,c)$ satisfying $a^7+b^7=7^c$
114489
Solving $x^p + y^p = p^z$ in positive integers $x,y,z$ and a prime $p$
98408
Show that $x^2+y^2+z^2=999$ has no integer solutions
31436
Show that for all $a\in\mathbb{N}$, there exists $b\in\mathbb{N}$ and square-free integer $c$ such that $\sqrt{a}=b\sqrt{c}$.
25258
Prove that if $ a,b,c > 0 $, then $ [(1 + a) (1 + b) (1 + c)]^{7} > 7^{7} (a^{4} b^{4} c^{4}) $.
47799
Show that the number or $r$ combinations of $X$ which contain no consecutive integers is given by $\binom{n-r+1}{r}$
45356
Are there any positive integers $a, b, c, d$ such that both $(a, b, c)$ and $(b, c, d)$ are Pythagorean triples?
71110
Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$
89677
Why there isn't any integer solutions in non-zero integers for $z^3 = 3(x^3 +y^3+2xyz)$?
69902
$3$ never divides $n^2+1$
111295
Prove that $a^7 + b^7 + c^7 \geq a^4b^3 + b^4c^3 + c^4a^3$
73079
Eliminating non-integer solutions to $ab / (2\sqrt{ab} + a + b)$
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
125040
Show by induction : $n^7-n$ is a multiple of 7
129163
Showing that every positive integer can be represented in this form
61987
$x^2+1=0$ in $\mathbb{Z}_7$
48127
Are there infinitely many $A\in \mathbb{C}^{2 \times 2}$ satisfying $A^3 = A$?
93606
Showing that $C[0,1]$ is not complete