Question

Show that one and only one out of n,n+2 or n+4 is divisible by 3whre NIS any positive integer

Answer 1

let n is equal to 3q + r( where 0>=r>3)

then r can be equal to 0, 1 or 2.

for r is equal to zero,
n = 3q divisible by 3
n + 2 = 3q + 2 not divisible by 3
n + 4 = 3q + 4
n + 4 = 3(q +1) +1 not divisible by 3

For r is equal to 1
n = 3q + 1 is not divisible by 3
n + 2 = 3q + 3
n + 2 = 3(q + 1) is divisible by 3
n + 4 = 3q + 5
n + 4 = 3(q + 1) +2 is not divisible by 3

For r is equal to 2
n = 3q + 2 is not divisible by 3
n + 2 = 3q + 4
n + 2 = 3(q + 1) + 1 is not divisible by 3
n + 4 = 3q + 6
n + 4 = 3(q + 2) is divisible by 3

Hence, Proved

hope it helps u
please mark as brainliest