Question

use Euclid's division lemma and show that any positive even integer is form of 6q or 6q+2 or 6q+4 where q is same integer..​

Answer 1

Answer:

Euclid division lemma :--> a = bq +r .

where r=> 0 or < b .

so , r is 4 .

r=0.

a=bq+r.

a=6q+0.

a=6q . even ...................i

r=1.

a=bq+r.

a= 6q+1.

r=2.

a=bq+r.

a=6q+2.

a= 2(3q+1)=> even...................ii

r=3.

a=bq+r.

a= 6q+3.

a=3(2q+1).=> odd ( because of odd number 3).

r=4.

a=bq+r.

a=6q+4.

a= 2(3q+2).=> even. ......................iii

SO, BY THE EQUATION i , ii , iii WE GET ALL POSITIVE INTEGER , IN THE FORM OF 6q FOR SOME INTEGER q .

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