
Re:    coprime integers
Posted:
Sep 27, 2011 7:35 PM


Deep <deepkdeb@yahoo.com> wrote: > > Let a, b be two coprime integers such that 2b > Statement: a, b, a+b, a  b are all coprime integers. > > Justification of the statement: > > There exista one prime p such that pa > Since pa 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 db then da iff dakb
Hence a, b and akb, b have the same set of common divisors d, hence the same *greatest* common divisor, i.e. gcd(a,b) = gcd(akb,b).
Bill Dubuque

