Suppose that a and b are positive integer then φ($a^b$) = a$^{b-1}$ φ(a)
94558
Show that $\phi(mn) = \phi(m)\phi(n)\frac{d}{\phi(d)}$
85977
Show that if $\sqrt{a}+\sqrt{b}\neq 0$, then $\mathbb{Q}(\sqrt{a}+\sqrt{b}) = \mathbb{Q}(\sqrt{a},\sqrt{b}), \forall a,b\in\mathbb{Q}$
127296
prove that a|b and b|a iff a=+-b
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
151434
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
6970
If $abc=1$ and $a,b,c$ are positive real numbers, prove that ${1 \over a+b+1} + {1 \over b+c+1} + {1 \over c+a+1} \le 1$.
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
131844
When does $(e^a)^b = e^{ab}$ hold?
13012
Why can a = b imply 2 = 1?
136854
Prove: For a,b,c positive integers, ac divides bc if and only if a divides b
98470
If $A \ne \varnothing$, then $\varnothing^A=\varnothing$
81346
Let $r$ be the smallest positive integer such that $a^r \equiv 1 \bmod{n}$. Prove $r \mid \phi(n)$.
14221
How can we prove it? ${a}{b}≤\frac{a^p}{p}+\frac{b^q}{q}$
104920
Can we find positive integers $a$ and $k \geq 2$ with $2^n - 1 = a^k$?
158844
If $a$ and $b$ are positive real numbers such that $a+b=1$, prove that $(a+1/a)^2+(b+1/b)^2\ge 25/2$