Find n if n = 3 mod 5, n = 1 mod 7, n = 0 mod 3.
N mod 5 = 3, N mod 7 = 1, N mod 3 = 0, solve for N
Using "Chinese Remainder Theorem + Modular Multiplicative Inverse", I obtained:
N = 105m + 78, where m=0, 1, 2, 3.....etc.