Question
What is the remainder when 7³⁵ is divided by
5?Solution
Using the cyclicity of powers of 7 modulo 5, observe the pattern: 7¹ ≡ 2 (mod 5), 7² ≡ 4 (mod 5), 7³ ≡ 3 (mod 5), 7⁴ ≡ 1 (mod 5). The pattern repeats every 4 terms. Since 35 ÷ 4 leaves a remainder of 3, 7³⁵ ≡ 7³ ≡ 3 (mod 5). Correct answer: c) 3
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