Question

Understanding this proof for the proposition "For all integers a, gcd(9a+4, 2a+1) = 1.

Proof: gcd(9a+4, 2a+1) = gcd(2a+1, a) = gcd(a, 1). Since gcd(a, 1)=1, gcd(9a+4, 2a+1) =1.

Answer 1

First line because 4(2a+1)=8a+4 and 9a+4-(8a+4)= a

Second line because a times 2 =2a and 2a+1-2a=1

Although the second equality is more or less obvious since 2a+1 leaves a remainder of 1 when divided by a.