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A number defined as the product of first $n$ prime numbers $+1$ is called $n$th Euclid number. Are there any survey on the progress for answering the following question: are there an infinite number ...

Related to this question and Alexander Kalmynin's answer. For natural $n$ define $J(n)=(2^{n-1}-1) \bmod n^2$ and if $n$ is power of two define $J(2^n)=1$ (this is artificial, just to avoid triviality ...

I posted this question on SE, and was told I should repost it here. The Goormaghtigh conjecture explores the Diophantine equation of the form $$ \frac{a^b-1}{a-1}=\frac{c^d-1}{c-1}, $$ where $a>c&...

Integer $n$ is Wieferich number if $2^{\phi(n)}-1 \equiv 0 \pmod {n^2}$. Wieferich prime is Wieferich number with $n$ prime. It is an open problem if there are infinitely many Wieferich primes and ...