Mathematics · Number Theory
For positive integers m and n, let gcd(m, n) denote their greatest common divisor. Let m > n be such that gcd(m, n) = 1. Which of the following statements is true regarding gcd(m - n, m + n)?
- 1gcd(m - n, m + n) can be an odd prime.
- 2There exist integers x and y such that nx - my = 3.
- 3gcd(m - n, m + n) can only be 1 or 2.✓
- 4gcd(m - n, m + n) must always be equal to 1.
Correct answer
gcd(m - n, m + n) can only be 1 or 2.
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