Question

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

Answer 1

 you can take any positive number

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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