Question
Find the remainder when 7²⁰² is divided by 100.
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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