Prove or disprove the statement If ab c N and ab bc and ac a

Prove or disprove the statement: If a,b, c N and ab, bc and ac all have the same parity, then a,b and c all have the same parity.

Solution

False

Counterexample

Let ab,bc and ac are all even

Let: a=3, b=2,c=4

ab=6,bc=8,ac=12 hence ab,bc and ac are all even but a=3 ie odd and b and c are even. Hence all three do not have the same parity