Computing remainders efficiently and understanding Fermat's Little Theorem.

This is where the "excursion" begins. Do not skip this even if you think you know algebra.

Simple number theory concepts—divisibility, primes, greatest common divisors, and modular arithmetic—introduce abstract properties of integers that have surprising applications (cryptography being a modern example at a more advanced level). Elementary combinatorics (counting principles, permutations, combinations) sharpens logical counting strategies and prepares students for probability and algorithmic thinking.