Mathematics · Number Theory
A positive integer n co-prime to 17 is called a primitive root modulo 17 if nk - 1 is not divisible by 17 for all k with 1 ≤ k < 16. Let a, b be distinct positive integers between 1 and 16. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The product of all primitive roots modulo 17 between 1 and 16 is congruent to 1 modulo 17
- 2If a, b are primitive roots modulo 17, then ab is a primitive root modulo 17
- 3If a is a primitive root modulo 17, then a2 is not necessarily a primitive root modulo 17✓
- 42 is a primitive root modulo 17
Correct answer
If a is a primitive root modulo 17, then a2 is not necessarily a primitive root modulo 17
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