Prove that g.c.d. (a-b, a+b) = 1 or 2, if g.c.d. (a,b) = 1

Asked by  | 1st Mar, 2013, 05:37: PM

Expert Answer:

Let d = gcd(a+b, a-b) > 0. We will show that d = 1 or 2.Since d is a divisor of a+b and a-b, it is a divisor of their sum as well as difference,  sum : (a+b) + (a-b) = 2a difference: (a+b) - (a-b) = 2b.Thus, since d is a divisor of both 2a and 2b, and yet the gcd of a and b is 1, then we're left with d = 1 or 2.

Aswered by  | 2nd Mar, 2013, 09:47: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.