Question

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

Answer 1

Heya!!!

↪ Here's your answer friend,

We know that any positive integer is in the form 3q, 3q + 1 or 3q + 2 where q is some integer.

Here, b = 3 therefore r = 0,1,2 as ( 0 >= b >r)

Therefore by Euclid's division lemma

we get,

for r = 0,

a = 3q + 0

==> a = 3q

again,

For r = 1,

==> a = 3q + 1

For r = 2,

==> a = 3q + 2

Therefore, we get that any positive integer is in the form of 3q, 3q + 1 or 3q + 2.


⭐ Hope it helps you : ) ⭐

Answer 2

$\huge \bf{ \red{hey}}$

$\huge{ \mathfrak{ \blue{here \: is \: answer}}}$

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

$\huge \boxed{ \boxed{ \green{HOPE\: IT \: HELPS}}}$

$\huge{ \pink{thanks}}$