Question

show that any positive even integer is of the form 8q , 8q+2 , 8q+4 or 8q+6 where q is some integer ???

Answer 1

to get even no the multiples of2 all are Even no.s
8 is multiple of 2 if we multiply any no with 2 the answer will be even it is only in the case of positive no.s
and adding no.s are also 2 multiples
for example q=1
8*1+2=8+2=10 and so on
hope this helps you quickly

Answer 2

Let a be any positive integer and b= 8. Using Euclid's Division lemma we get a=8q+r where 0≤ r < 8. so the possible values of remainders are 0, 1, 2, 3, 4, 5, 6 and 7. So, 'a' can be of the form 8q, 8q+1, 8q+2, 8q+3, 8q+4, 8q+5, 8q+6 or 8q+7. 

But it is given that the positive integer must be even. So a can not be 8q+1, 8q+3, 8q+5, 8q+7 (Since these values are odd)

Therefore any positive even integer can be represented in the form 8q, 8q+2, 8q+ 4 or 8q+ 6. 

Hope this helps!! Please mark it as brainliest!