Question

show that any postive integer is ofthe form of3q or 3q+1 or 3q+2 for some integer q

Answer 1

Euclid's Division Lemma : For any two positive integers a and b, there exists two unique integers q and r such that a = bq + r, 0r < b.

If we take b = 3, the possible values of r will be 0, 1 and 2

Hence, either a = 3q or a = 3q + 1 or a = 3q + 2.

Hope u got

Answer 2

Hey there!
The answer:-


Let n be any positive integer
on dividing n by 3 let q be the quotient and r be the remainder.
Then, By Euclid's division lemma

n=3q+r. where 0<= r< 3
so, r=1,2,3

◆when r=0
Then, n=3q

◆when r=1
Then, n=3q+1

◆when r=2
Then, n=3q+2


There fore any positive integer is of the form 3q or 3q+1 or 3q+2



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