Question

Show that any positive even integer is of the form 6q,6q + 2 or 6q + 4, where q is some integer.

Answer 1

every multiple of six is an even number...
an even number + another even number is always an even number

Answer 2

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

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

let a be any positive integer

then

b= 6

a= bq+r

0≤r<b

0≤r<6

r= 0,1,2,3,4,5

case 1.

r=0

a= bq+r

6q+0

6q

case 2.

r=1

a= 6q+1

6q+1

case3.

r=2

a=6q+2

case 4.

r=3

a=6q+3

case 5

r=4

a=6q+4

case 6..

r=5

a=6q+5

hence from above it is proved that any positive integer is of the form 6q, 6q+1,6q+2,6q+3,6q+4 and 6q+5and

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

$\huge{ \pink{thanks}}$