Number theory toolkit: sieve of Eratosthenes, fast modular exponentiation, and gcd.
Sieving primes, fast modular power, and Euclid's gcd are the number-theory primitives that quietly drive crypto, hashing, and combinatorics problems. The signal is the O(n log log n) sieve and O(log e) binary exponentiation. Here is the answer.
Updated Sep 2026 · Grounded in real GenAI, LLM, and AI/ML engineering interview loops and written to a senior-engineer editorial bar.
Sieving primes, fast modular power, and Euclid's gcd are the number-theory primitives that quietly drive crypto, hashing, and combinatorics problems. The signal is the O(n log log n) sieve and O(log e) binary exponentiation. Here is the answer.
Lead with where the obvious approach breaks, because that is the judgment they are screening for — most candidates jump straight to the happy path and lose the room.
Then walk the failure back through the pipeline in order, naming the one metric the customer's exec sponsor actually cares about before you propose the fix.
