Question

Show that one and only one out of n,(n+1)and(n+2) is divisible by 3 where n is an positive integer
plzz do it step by step​

Answer 1

Let a = n be a positive integer b = 3

By Euclid's division lemma a = bq + r where

$0 \leqslant r < b$

r = 0 , 1 , 2 because

$0 \leqslant r < 3$

If r = 0 ; then a = 3q

n = 3q

If r = 1 ; then a = 3q + 1

n = 3q + 1

n + 1 = 3q + 1 + 1

n + 1 = 3q + 2

If r = 2 ; then a = 3q + 2

n = 3q + 2

n + 2 = 3q + 2 + 2

n + 2 = 3q + 4

Therefore only one out of n , (n + 1) & (n + 2) only n is divisible....

But ( n + 2 ) & (n + 4 ) will be divisible .....