MathNet 2021 — Part 07 Question 13

Determine the number of ordered triples $(a,b,c)$ of nonnegative integers such that each of $2^a$, $2^b$, and $2^c$ is less than $10000$, and $2^a+2^b+2^c$ is a divisor of $8^a+8^b+8^c$.