Question

Show that exactly one of the number of n, n+2,n+4 is divisible by 3

Answer 1

this is your answer of this question

Answer 2

Let n be any number which is divided by 3 gives q as quotient and r as remainder.

Then by Euclid's division lemma

that is,
=> a = bq+r

so,

n = 3q+r

Where,
0≤ r < 3
r = 0,1,2

then,

n = 3q

n = 3q+1

n = 3q+2

⭐Case -1

n = 3q

:- it is divisible by 3

⭐Case -2

n = 3q+1

n+2 = 3q+1+2

n+2 = 3q+3

n+2 = 3(q+1)

:- It is divisible by 3

⭐Case -3

n=3q+2

n+4 = 3q+2+4

n+4 = 3q+6

n+4 = 3(q+2)

:- it is also divisible by 3