2 problems

For an integer $k\geq0$, let … denote the number of positive divisors of $n$. Merca's conjecture. If … for every $n\geq0$, then there is a sequence of prime numbers…

Let $p>2$ be prime, and let $A'$ and $B'$ be coprime integers. A Ramanujan-type congruence for Euler's totient function $cvarphi$ would have the form … for every $n\geq0$. The toti…