Question

2. Prove that one of every three consecutive positive integers is divisible by 3​

Answer 1

Answer:

Let a, a+1, a+2 be the three consecutive positive integers.

Then, a is of the 3q, 3q+1, 3q+2 .

When a=3q

therefore, a = 3q

It is divisible by 3.

when a =3q+1

therefore, a+2 =3q+1 +2

= 3q+3

=3(q+1)

=3k, k =q+1 is an integer.

It is divisible by 3.

when, a=3q+2

therefore , a+1= 3q+2+1

=3q+3

=3(q+1)

3k, k= q+1 is an integer.

It is divisible by 3.

Hence, one of the three consecutive positive integers is divisible by 3.

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