Find the smallest positive integer that leaves remainder 3 when divided by 4 and remainder 2 when divided by 5.
Note
Numbers congruent to 3 mod 4 are 4k+3; solving 4k+3 ≡ 2 (mod 5) gives k ≡ 1 (mod 5) so k=1 yields 4·1+3 = 7, the smallest such positive integer.