For every odd $n \in \mathbb{N}$ prove that $\phi(n)$ is not equal $2^{32}$
114136
Euler's $\phi(n)$ function and solutions of $\phi(n) = 4294967296=2^{32}$
18953
Prove that even + odd is odd.
9753
How to solve the equation $\phi(n) = k$?
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
46147
Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
50940
Prove $1^{2007}+2^{2007}+\cdots+n^{2007}$ is not divisible by $n+2$
24403
Prove that $ n < 2^{n}$ for all natural numbers $n$.
99037
Prove the sum of all numbers that do not have a multiplicative inverse mod $n$
107725
Prove that if $n$ is not divisible by $5$, then $n^4 \equiv 1 \pmod{5}$
97411
If $x^n=y^n$ and $n$ is odd then $x=y$
156766
Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
138819
Prove that $\phi(n) \geq \sqrt{n}/2$
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$
52542
For which odd positive integer $n$ , is it true that $-1$ is not a positive power of $2$ modulo $n$?
43940
Showing that $n$ is pseudoprime to the base $a$
17047
Prove that if n is even then $n^2$ is even and if n is odd then $n^2$ is odd?
47790
If $x \geq 2$ prove that $\sum_{ n \leq x} \frac{1}{\phi(n)} = \mathcal{O}(\log(x))$