Question

Show that any positive integer is of the form 3q or 3q + 1 or 3 q plus two f o r some integer q

Answer 1

HOLA

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Let N be an arbitary integer

On diving n by 3 we get quotient Q and remainder R

So we have ( 3q ) , ( 3q + 1 ) , ( 3q + 2 )

So now we have

1st Case -- ( 3q ) which is clearly positive

2nd case -- ( 3q + 1 ) clearly positive

3rd case -- ( 3q + 2 ) clearly positive


So any of the form ( 3q ) , ( 3q + 1 ) , ( 3q + 2 ) is clearly a positive integer

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HOPE U UNDERSTAND ❤❤❤

Answer 2

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let a be any positive integer

then

b= 3

a= bq+r

0≤r<b

0≤r<3

r= 0,1,2

case 1.

r=0

a= bq+r

3q+0

3q

case 2.

r=1

a= 3q+1

3q+1

case3.

r=2

a=3q+2

hence from above it is proved that any positive integer is of the form 3q,3q+1 and 3q+2

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