Find all integers $n>1$ such that $n^2|2^n+1$.
12967
Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer.
27063
Prove that if n is an odd positive integer , then $n^2\equiv1\mod8$
26912
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$
15604
Determine the set of points $z$ that satisfy the condition $|2z|>|1+z^2|$
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
5043
Show that $2^n>1+n\sqrt{2^{n-1}}$
130093
Prove by Induction : $n < 2^n$
18053
Find all prime $p$ such that $x^2=-1$ has a solution in $\mathbb{Z}/p\mathbb{Z}$
29811
Find all polynomials $P$ such that $P(x^2+1)=P(x)^2+1$
55266
Prove that $(n+1)^{n-1}<n^n$
77547
Find integers $a,b,c,d$ such that
118197
Solve $n(n+1)(n+2)=6m^3$ in positive integers
63129
Infinite number of $k$ satisfying $p_{k+1} - p_{k} > 2$?
50781
$(n+1)$th prime $p_{n+1}$ less than or equal to $p_1p_2\dots p_n+1$
75166
Find with proof all positive integers $n$ such that $2^n + 1 \equiv 0 \pmod{n}$
77564
How to prove for each positive integer $n$, the sum of the first $n$ odd positive integers is $n^2$?
8504
Factoring $x^n + y^n$ over the integers