Finding all possible pairs of integers $(a,b)$ such that $a^b=n$.
40312
How to quickly identify perfect powers
124223
Find all pairs (x, y) of real numbers such that $16^{x^2+y} + 16^{x+y^2}=1$
2522
Why is $a^n - b^n$ divisible by $a-b$?
126280
In a P.I.D., if $a^m = b^m$ and $a^n = b^n$ for $m, n \in \mathbb{N}$ with $\gcd(m,n) = 1$, then $a=b$
92057
Prove that for every odd integer n, there is a group...
52951
Find all $n \in \mathbb{Z^+}$ such that $\phi(n)=4$
28861
Given an invertible matrix $A$ such that all elements in $A$ and in $𝐴^{−1}$ are integers, find $|𝐴^4|$
66358
Prove by mathematical induction that $2n ≤ 2^n$, for all integer $n≥1$?
114404
For which positive integer values of $n$ does $a|mn-b?$
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
75166
Find with proof all positive integers $n$ such that $2^n + 1 \equiv 0 \pmod{n}$
8884
Find all natural numbers $n$ and $m$ for which $n^m=(n-1)!+1$
21781
Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$
45454
Pairs of $(p,q)$ such that $p^2 + 1 = 2 q^2$?
48211
When is $(a+b)^n \equiv a^n+b^n$?
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
148906
Finding integers $m,n$ such that $(m-n)^2=4mn/(m+n-1)$