coprimality

Mathematics

Number Theory & Cryptography

• Euler's Totient and TheoremMultiplication modulo n sometimes loses information. Multiplication by a number coprime to n does the opposite: it rearranges all the invertible residues without merging any. Euler's theorem is a consequence of that rearrangement.
• GCD and the Euclidean AlgorithmImagine cutting two ropes into equal-length pieces without leaving a remainder. The longest possible piece length is their greatest common divisor, abbreviated gcd. For integers, divisors are exact: 6 divides both 48 and 18, and no larger positive integer does.