JEE Main 2024 Mathematics question

The remainder when 428²⁰²⁴ is divided by 21 is .........

Answer: 1

Solution

428 = 420 + 8 = 21 × 20 + 8, so 428²⁰²⁴ ≡ 8²⁰²⁴ (mod 21). Now 8²⁰²⁴ = 64¹⁰¹²

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Question ID VK-016559