Prove a b g c d a4g c d b42 right arrow g c d ab 4Solutionsi

Prove: a, b (g c d (a,4)=g c d (b,4)=2 right arrow g c d (a+b, 4).

Solution

since the gcd(a,4) = 2

that is a must be even number but can not be multiple of 4,because if it is multiple of 4 then gcd will be 4.

so only possible possibility of a is 2.

similarly

since the gcd(b,4) = 2

that is b must be even number but can not be multiple of 4. because if it is multiple of 4 then gcd will be 4.

so only possible possibility of b is 2.

then gcd (a+b,4) = gcd (2+2, 4) = gcd (4,4) = 4

hence proved.