Arrange the following in ascending order:
(a) Remainder of 4916 when divided by 17
(b) Remainder of 2446 when divided by 9
(c) Remainder of 15517 when divided by 17
(d) Last digit of the number 745
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Correct answer: C. (a), (c), (b), (d)
Explanation
(a) 49 ≡ −2 (mod 17), so (−2)16 = 164 ≡ (−1)4 = 1. (b) 26 ≡ 1 (mod 9) and 446 = 6·74 + 2, so the remainder is 4. (c) By Fermat, 15517 ≡ 155 ≡ 2 (mod 17). (d) Last digits of powers of 7 cycle 7, 9, 3, 1, and 45 ≡ 1 (mod 4), so 7. Order: 1 (a), 2 (c), 4 (b), 7 (d).More Discrete Structures and Optimization questions
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