Congruences

Question 1

a is congruent to b modulo m

Answer 1

m divides b-a

Question 2

congruence class [a]

Answer 2

coset of the ideal mZ

Question 3

weak cancellation law

Answer 3

ka=kb mode iff a=b mod(m/d)

Question 4

Euler’s theorem

Answer 4

if gcd(a,m)=1 then a^(φ(m))=1 modm

Question 5

Fermat’s Little Theorem

Answer 5

if p prime, a^p=a mod p

Question 6

Chinese Remainder Theorem

Answer 6

m,n coprime then the pair of congruences has a unique solution