Question

Show that any positive integer in the form of 3q or 3 cube + 1 or 3 cube + 2 for some integer q

Answer 1

HOLA

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Let N be an arbitrary integer

On dividing N by 3 we get qoutient M and remainder R

By Euclid's division lemma

3m , 3m + 1 , 3m + 2.

Hence any number of the form 3m , 3m + 1 , 3m + 2 Can be a positive integer

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HOPE U UNDERSTAND ☺☺☺☺

Answer 2

Let a be any positive integer
When a is divided by 3 we get q as our quotient and r as our remainder
=a=3q +r - (i)
Here r=0,1,2
Put r=0 in equation i
=3q
Put r=1 in equation i
3q+1
Put r=2in equation i
3q+2

Hence proved