Question

If a is an odd integer then prove that gcd(3a,3a+2)=1​

Answer 1

Answer:

6a+2=1

6a=1+2

6a=3

a=3/6

a=1/2 answer

Answer 2

Answer:

Since a is odd, 3a is also odd. [ For example, if a=3, 3a = 9 is odd, if a=11, 3a = 33 is odd and so on].

Any odd number added with 2 gives you the next odd number. In other words, the sequence of odd numbers has a common difference of 2.

Thus, 3a+2 is the odd number next to 3a.

Since any two consecutive odd numbers are relatively prime [for example, (9,11), (27,29), (45,47), etc.] (i.e., they have no common factors other than 1) , GCD(3a,3a+2) = 1.

Step-by-step explanation:

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