Unit · year 2
MU-207 · Number Theory
Threads number5 theorems
The deep structure of the integers, from unique factorisation to reciprocity.
Theorems in this unit
T-074
The Euclidean algorithm and Bézout's identity
The gcd is an integer combination of its arguments.
T-075
The fundamental theorem of arithmetic
Every integer factors uniquely into primes.
T-076
Euler's theorem
a^φ(n) ≡ 1 (mod n) for a coprime to n.
T-077
Wilson's theorem
(p−1)! ≡ −1 (mod p) exactly when p is prime.
T-078
The law of quadratic reciprocity
A reciprocal relationship between two primes being squares mod each other.