Math & Number Theory Interview Questions & Solutions

Math-flavored interview problems reward recognizing the right numerical insight rather than grinding out brute force. They cover primes and the sieve of Eratosthenes, greatest common divisors via the Euclidean algorithm, modular arithmetic for keeping huge intermediate results in range, and the integer-overflow pitfalls that catch candidates who don't think about bounds. Often a problem that looks like it needs a loop over billions of values collapses to a formula or a logarithmic trick.

These solutions also fold in divide-and-conquer — the broader strategy of splitting a problem into independent halves, solving each, and combining — since fast exponentiation, integer square roots, and several classic math questions are solved exactly that way. For each problem we surface the underlying property (why the Euclidean algorithm terminates, why fast power is O(log n), how to multiply safely under a modulus) so the solution is something you can reconstruct, not just recall. These questions appear less often than the core data-structure patterns, but they're where a little number-theory fluency turns an intimidating prompt into a few clean lines.