Name:

[2pts] Use the trial division algorithm to find the prime factorization for the following numbers:

6300

2080

[2pts] Use the Euclidean Algorithm to find the GCD of the following:

gcd〖(900,270)〗

gcd〖(154,165)〗

[3pts] Prove Theorem 4.4.1: Let m∈Z^+ and a,b,c∈Z. If (i) ac≡bc(mod m) and (ii) gcd(c, m)=1 then a≡b(mod m)

[3pts] Prove the Chinese Remainder Theorem