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.