Find the smallest positive integer x such that 3x + 1 is divisible by 7.
Note
Solve 3x + 1 ≡ 0 (mod 7) ⇒ 3x ≡ 6 (mod 7). The inverse of 3 mod 7 is 5, so x ≡ 5·6 ≡ 30 ≡ 2 (mod 7); smallest positive x = 2.
Find the smallest positive integer x such that 3x + 1 is divisible by 7.
Solve 3x + 1 ≡ 0 (mod 7) ⇒ 3x ≡ 6 (mod 7). The inverse of 3 mod 7 is 5, so x ≡ 5·6 ≡ 30 ≡ 2 (mod 7); smallest positive x = 2.