Arrange the following in ascending order: (a) remainder of 49¹⁶ divided by 17 (b) remainder of 24⁴⁶ divided by 9 (c) remainder of 155¹⁷ divided by 17 (d) last digit of 7⁴⁵

Explanation

(a) 49 ≡ −2 (mod 17) and 2⁴ ≡ −1, so 2¹⁶ ≡ 1. (b) 24 ≡ 6 (mod 9) and 6² = 36 ≡ 0, so the remainder is 0. (c) 155 ≡ 2 (mod 17); by Fermat 2¹⁷ ≡ 2. (d) Powers of 7 end in 7, 9, 3, 1; 45 ≡ 1 (mod 4) gives 7.

Note: no option is fully correct; the official key (C) is shown. The values are (a) 1, (b) 0, (c) 2, (d) 7, giving the order (b), (a), (c), (d), which is not among the options. The official key is C.