Question 13
Given two positive integers $a$ and $b$, $(a \nabla b)$ denotes the remainder obtained by dividing $a$ by $b$. This residue is one of the numbers $0, 1, \ldots, b-1$. Find all pairs of numbers $(a, p)$ such that $p$ is prime and it holds that
$$
(a \nabla p) + (a \nabla 2p) + (a \nabla 3p) + (a \nabla 4p) = a + p.
$$
$$
(a \nabla p) + (a \nabla 2p) + (a \nabla 3p) + (a \nabla 4p) = a + p.
$$