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.

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.