What does it mean for two numbers to share a divisor — and how do you find the largest one without factoring? The Euclidean Algorithm, proved from scratch.
The GCD is not just a maximum — it is the smallest linear combination of two integers. Bezout's Identity reframes everything, and Euclid's Lemma follows from it.
Seven identities that reduce hard GCD problems to one-line arguments — including the power identity, Fibonacci GCD, and Euclid's Lemma. Each with a proof short enough to reconstruct on the spot.
When does ax + by = c have integer solutions? When it does, how many, and how do you find them all? Complete theory including the Frobenius number for two coprime integers.
GCD determines which linear congruences are solvable, how many solutions they have, and when inverses exist modulo m. Includes Euler's totient and the Chinese Remainder Theorem.
14 graded problems from direct computation to olympiad-adjacent. Each solution names the exact tool it uses, with a quick-reference table at the end.