Remainders of $5^{102}$ and $3^{104}$ upon division by $103$

This is Problem 4.118 of N. B. Alfutova and A. V. Ustinov, Algebra and Number Theory (MCCME, 2002), Chapter 4, §4 “Theorems of Fermat and Euler”. The problem asks for the remainders upon division by $103$ of the numbers (a) $5^{102}$ and (b) $3^{104}$. The book's answers are $1$ and $9$.

Theorem.

Since $103$ is prime, the exercise illustrates Fermat's little theorem $a^{102}\equiv 1 \pmod{103}$ for $103\nmid a$.

Formalization Note The remainders are computed with natural-number division with remainder (%) on $\mathbb N$.