Deep <firstname.lastname@example.org> wrote: > > Let a, b be two coprime integers such that 2|b > Statement: a, b, a+b, a - b are all coprime integers. > > Justification of the statement: > > There exista one prime p such that p|a > Since p|a and p doesnot divide b then p cannot divide (a + b). > By similar argument p does not divide(a - b). > Consequently, a, b, a + b, a - b are all coprime integers. > > Any comment about the ccorrectness of the Statement will be > appreciated.
HINT If d|b then d|a iff d|a-kb
Hence a, b and a-kb, b have the same set of common divisors d, hence the same *greatest* common divisor, i.e. gcd(a,b) = gcd(a-kb,b).