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    Question

    Find the remainder when 7²⁰² is divided by 100.

    A 30 Correct Answer Incorrect Answer
    B 77 Correct Answer Incorrect Answer
    C 49 Correct Answer Incorrect Answer
    D 23 Correct Answer Incorrect Answer

    Solution

    Note: 7² = 49 7⁴ = 49² = 2401 ≡ 1 (mod 100) So 7⁴ ≡ 1 (mod 100) Now 202 = 4×50 + 2 7²⁰² = 7^(4×50+2) = (7⁴)⁵⁰ × 7² ≡ 1⁵⁰ × 7² (mod 100) ≡ 49 (mod 100) Remainder = 49.

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