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    Question

    What is the remainder when 7³⁵ is divided by

    5?
    A 1 Correct Answer Incorrect Answer
    B 2 Correct Answer Incorrect Answer
    C 3 Correct Answer Incorrect Answer
    D 4 Correct Answer Incorrect Answer

    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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