7. Show that any positive even integer can be written in the form 6q,+

1.	7. Show that any positive even integer can be written in the form 6q,+ 2 or 6q + 4, where q is an2
Answer» Let a be the positive odd integer which when divided by 6 gives q as quotient and r as remainder. according to Euclid's division lemmaa=bq+r a=6q+r where , a=0,1,2,3,4,5then,a=6qora=6q+1ora=6q+2ora=6q+3ora=6q+4ora=6q+5 but here,a=6q+1 & a=6q+3 & a=6q+5 are odd.

7. Show that any positive even integer can be written in the form 6q,+ 2 or 6q + 4, where q is an2

Answer»

Let a be the positive odd integer which when divided by 6 gives q as quotient and r as remainder.

according to Euclid's division lemmaa=bq+r

a=6q+r

where , a=0,1,2,3,4,5then,a=6qora=6q+1ora=6q+2ora=6q+3ora=6q+4ora=6q+5

but here,a=6q+1 & a=6q+3 & a=6q+5 are odd.