Question

6n+2+72n+1 is divisible by 43

Answer 1

6n+2+72n+1
= 6n x 6² + (7²)n x 7
= 6n x 36 + 49n x 7 ≡ [6n x 36 + (6)n x 7] (mod 43) ≡ [6n X (36+7)] (mod 43)
≡ [6n x (43)] (mod 43) ≡ [6n x (0)] (mod 43) ≡ 0 x (mod 43)
Hence, 6n+2 + 72n+1 = 0(mod 43)
Therefore, 6n+2 + 72n+1 is divisible by 43