The value of 351 mod 5 is ________.
2019
The value of 351 mod 5 is ________.
Attempted by 3 students.
Show answer & explanation
Correct answer: 2
Key idea: Powers of 3 modulo 5 repeat with period 4 because 3^4 ≡ 1 (mod 5).
Compute the cycle: 3^1 ≡ 3, 3^2 ≡ 4, 3^3 ≡ 2, 3^4 ≡ 1 (all mod 5).
Reduce the exponent 51 modulo the cycle length 4: 51 ≡ 3 (mod 4).
So 3^51 ≡ 3^3 ≡ 27 ≡ 2 (mod 5).
Therefore the value of 3^51 mod 5 is 2.