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What is the smallest positive integer n for which 2^n ≡ 1... | QuestionStock

Representative image for question: What is the smallest positive integer n for which 2^n ≡ 1 (mod 7)?

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Mathematics

What is the smallest positive integer n for which 2^n ≡ 1 (mod 7)?

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What is the smallest positive integer n for which 2^n ≡ 1 (mod 7)?

Options:

1
2
3
6

Correct answer: 3

Explanation: Compute powers: 2^1=2, 2^2=4, and 2^3=8 ≡ 1 (mod 7); thus the multiplicative order of 2 modulo 7 is n = 3, since 2^3 = 8.

Created 2026-03-10T18:03:05.030Z. Updated 2026-03-10T18:03:05.030Z.