Question

show that only one of three consecutive integers is divisible by 3

Answer 1

Any three consecutive integers cannot be the multiple of 3 because every multiple of 3 has a difference of 3 between them.
For Example -
3 × 1 = 3
3 × 2 = 6
3 × 3 = 9

and 3, 6, 9 have difference of 3 with each other.