Prove Euler's Theorem when the integers are not relatively prime
49938
Proof of $a^{\phi (n) +1} \equiv a \pmod{\! n} $ Carmichael generalization of Fermat-Euler's theorem.
45460
Proof verification of a number theory problem involving sequences.
95653
Euler's theorem: [3]^2014^2014 mod 98
61899
Prove that the language $\{bin(p) \mid p\ \text{is prime}\}$ is not regular (prime numbers)
45127
Why is Euler's totient function equal to $(p-1)(q-1)$ when $N=pq$ and $p$ and $q$ are prime in a clean intuitive way?
80658
Prove that the number $19\cdot8^n+17$ is not prime, $n\in\mathbb{Z}^+$
131479
How do I prove that 15462227 and 15462229 relatively prime?
125188
how to prove $m^{\phi(n)}+n^{\phi(m)}\equiv 1 \pmod{mn}$ where m and n are relatively prime?
144622
Proof: If no prime less than or equal to $\sqrt{n}$ divides $n$, then $n$ is a prime
106157
Proof of Euclid's lemma using fundamental theorem of arithmetic
75516
Relatively Prime Numbers and Number of Divisors of n
39915
Let $n$ be an integer such that if $d | n$ then $d + 1 | n + 1.$ Show that $n$ is a prime number
12862
Prove that two distinct numbers of the form $a^{2^{n}} + 1$ and $a^{2^{m}} + 1$ are relatively prime if $a$ is even and have $\gcd=2$ if $a$ is odd
143772
How can I algebraically prove that $2^n - 1$ is not always prime?
156766
Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
149589
Analogous results to Euler's theorem
344
Prove that if $p\in \mathbb{Z}$ is irreducible, then it is also prime.