Question

Show that exactly one of that umbers n, n+2 or n+4 is divisible by 3

Answer 1

for n=4. n+2 =6 which is divisible by 3.


n+(n+2)+(n+4)=3n+6 =3 (n+1).

Hence, one of these is divisible by three .

Answer 2

ANSWER

Case I:

If n=3q

n+4=3q+4

n+2=3q+2

here n is only divisible by 3

Case II:

If n=3q+1

n+4=3q+5

n+2=3q+3=3(q+1)

Here only n+2 is divisible by 3

Case III:

If n=3q+2

n+2=3q+4

n+4=3q+2+4 =3q+6

Here only n+4 is divisible by 3

Hence, only one of the numbers n,n+2,n+4 is divisible by 3.

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