Question

Prove that only one of the number n-1, n+1 or n+5 is divisible by 3, where n is any positive integer. Explain

Answer 1

we can writen as
for any positive integer n =3q, 3q+1, 3q+2

for n+1

(3q)+1 - not divisible by 3
(3q+1)+1=3q+2 - not divisible by 3
(3q+2)+1=3q+3 - divisible by 3

for n-1
(3q)-1 -not divisible by 3
(3q+1)-1=3q -divisible by 3
(3q+2)-1=3q+1 -not divisible by3

​for n+5
(3q)+5 -not divisible by 3
(3q+1)+5 =3q+6 -divisible by 3
(3q+2)+5=3q+7 -not divisible by 3