Question

show that exactly one of the number N,N + 2 or N + 4 is divisible by 3

Answer 1

let n be 3 the...the other two vl be 5 and 7

Answer 2

Hey user !!

Here's the answer you are looking for

Let N = 3q + r where q and r are any positive integers and 0≤r<3.

☛ CASE 1 (r = 0)
N = 3q
N + 2 = 3q + 2
N + 4 = 3q + 4

Out of these, only N is divisible by 3.

☛ CASE 2 ( r = 1)

N = 3q + 1
N + 2 = 3q + 3
N + 4 = 3q + 5

Out of these only (N + 2) is divisible by 3

☛ CASE 3 (r = 2)

N = 3q + 2
N + 2 = 3q + 4
N + 4 = 3q + 6

Out of these, only (N + 4) is divisible by 3.

Therefore, exactly one of the number N,N + 2 or N + 4 is divisible by 3.


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