Question

Prove that one of every three consecutive positive integer is divisible by 3​

Answer 1

Solution :

let n, n+1, n+2 be the three consecutive positive integers.

we know that n is in the form of 3q, 3q+1, 3q+2.

Case -1, when n=3q

n is divisibe nut n+1 & n+2 are not divisible.

Case-2, when n=3q+1

n+2= 3q+3= 3(q+1) it is divisible by 3

but n+1 & n are not divisible by 3 Case-3, when 3q+2

n+1= 3q+3 = 3(q+1) it is divisible by 3

but n+2 & n are not divisible

hence none of the situation is possible for 3 consecutive no divisible by 3.

Answer 2

Answer:

$\: \: \: \: \: \: \: \: \: \:$

Prove that one of every three consecutive positive integer is divisible by 3 .

Top answer · 239 votes

Let n,n + 1,n + 2 be three consecutive positive integers.We know that n is of the form 3q,3q + 1 or, 3q + 2 (As per Euclid Division Lemma),