Proofs Question Prove that if a b and c are three consecutiv

Proofs Question

Prove that, if a, b and c are three consecutive odd integers, with a

Solution

LEt, a,b,c be

2k-1,2k+1,2k+3

So,

b-a=2 mod 3

c-b=2 mod 3

c-a=4=1 mod 3

Hence all three of them give them different remainder modulo 3

But there are only three remainders modulo 3

SO one of them and only one of them is a multiple of 3