Multiple choice general knowledge math & puzzles

What is the remainder when 7^123 is divided by 48

  1. 7

  2. 1

  3. 23

  4. 11
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A Correct answer
Explanation

Use Euler's theorem: 7 and 48 are not coprime (gcd=7), but observe the pattern: 7^1 ≡ 7 (mod 48), 7^2 = 49 ≡ 1 (mod 48), 7^3 = 7×1 ≡ 7 (mod 48), 7^4 = 7×7 = 49 ≡ 1 (mod 48). The pattern repeats every 2: odd exponents give remainder 7, even exponents give remainder 1. Since 123 is odd, the remainder is 7.

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