Find the remainder when 2^10 is divided by 7.
Note
Since 2^3 ≡ 1 (mod 7), 2^10 = (2^3)^3×2 ≡ 1^3×2 ≡ 2 (mod 7), so the remainder is 2.
Find the remainder when 2^10 is divided by 7.
Since 2^3 ≡ 1 (mod 7), 2^10 = (2^3)^3×2 ≡ 1^3×2 ≡ 2 (mod 7), so the remainder is 2.