Statement I: 5 divides n⁵ − n whenever n is a non-negative integer. Statement II: 6 divides n³ − n whenever n is a non-negative integer.

1. ABoth Statement I and Statement II are correct
2. BBoth Statement I and Statement II are incorrect
3. CStatement I is correct but Statement II is incorrect
4. DStatement I is incorrect but Statement II is correct

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: A. Both Statement I and Statement II are correct

Explanation

n⁵ ≡ n (mod 5) by Fermat's little theorem. n³ − n = (n − 1)n(n + 1), a product of three consecutive integers, so it is divisible by 6. Both true.