Answer to Question #96098 in Combinatorics | Number Theory for Dina

Question

Let a and b be relatively prime integers. Find all values of (a + 2b, a − 2b).

Answer 1

a and b are relatively prime numbers, then Their GCD is equals to 1

Gcd (a, b ) = 1

(or)

(a, b) = 1 ( These two are the notations to denote relatively prime numbers)

the only divisor of both the numbers a and b is 1

Let d = (a + 2b, a − 2b)

means d divides a + 2b and d divides a - 2b

If d | x and d | y then d | ( x- y) and d | ( y - x),

that is, d | (a+2b) and d | ( a-2b).

So, d | (a + 2b + a - 2b) and d | (a - 2b - a - 2b)

d| (2a) and d | (-4b)

d| 2

the numbers 1, 2 divide 2

So, d = 1 or 2.