Question
Find the remainder when 215 is divided by
7.Solution
ATQ, Calculate powers of 2 mod 7: 21 = 2 (mod 7) 22 = 4 (mod 7) 23 = 8 ≡ 1 (mod 7) So pattern repeats every 3 powers: 2, 4, 1, 2, 4, 1, ... 15 ÷ 3 = 5, remainder 0 So 215 will give the same remainder as 23 (end of a full cycle), which is 1.
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