5 problems

Let $A=2^n abcd$ and $B=2^n efgh$ be a symmetric higher-order amicable pair, with $a,b,c,d,e,f,g,h$ denoting the relevant prime factors. Define $x$ and $y$ through the normalized e…

Sum of amicable numbers conjecture. As the largest number in an amicable pair approaches infinity, the percentage of sums of amicable pairs divisible by $10$ approaches $100\%$.

Coprime feebly amicable pairs conjecture. There are infinitely many coprime feebly amicable pairs.

Let $(M,N)$ be an amicable pair, meaning distinct positive integers satisfying … and suppose that $M$ and $N$ are relatively prime. Gmelin's conjecture. There is no relatively prim…

Pomerance's upper-bound conjecture. Pomerance's constant satisfies