Assuming that gcd(a, b) = 1, prove the following:
(a) gcd(a + b, a − b) = 1 or 2.
[Hint: Let d = gcd(a + b, a − b) and show that d|2a, d|2b, and thus that d ≤ gcd(2a, 2b) = 2 gcd(a, b).]
(b) gcd(2a + b, a + 2b) − 1 or 3.
(c) gcd(a + b, a2 + b2) = 1 or 2.
[Hint: a2 + b2 = (a + b)(a − b) + 2b2.]
(d) gcd(a + b, a2 − ab + b2) = 1 or 3.
[Hint: a2 − ab + b2 = (a + b)2 − 3ab.]
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.