1.2.2) gcd(a,b) = p(prime), gcd(a^2, b), gcd(a^3, b^2) ?
note1: a, b E Z, gcd(a, b) = c -> gcd(a^2, b^2) = c^2
note2: gcd(a, b) = p -> p = as + bt, s, t E Z
let gcd(a^2, b) = p`
p` = (a^2)s + bt
p = as + bt
p^2 = (a^2)s + (b^2)t
p + (p^2) - (as + (b^2)t) = (a^2)s + bt = p`
let gcd(a^3, b^2) = p``
p`` = (a^3)s + (b^2)t
(a+1)(p^2) - ( (a^2)s + a(b^2)t ) = (a^3)s + (b^2)t = p``
ISBN 978-89-5526-658-0
17pg 1.2.2 no sol
