Math  /  Numbers & Operations

Question4. Assuming that gcd(a,b)=1\operatorname{gcd}(a, b)=1, prove the following: (b) gcd(2a+b,a+2b)=1\operatorname{gcd}(2 a+b, a+2 b)=1 or 3 .

Studdy Solution
Conclude the proof by considering the possible gcd values. Since gcd(a+2b,3)\operatorname{gcd}(a + 2b, 3) must divide 3, the possible values are 1 or 3.
Thus, gcd(2a+b,a+2b)=1\operatorname{gcd}(2a + b, a + 2b) = 1 or 33.
The proof is complete. The gcd is either 11 or 33.

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