Question

Show that any positive integer is in the form of 6q+1,6q+3 or 6q+5 where q is any integer

Answer 1

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 lemma

a=bq+r

a=6q+r

where , a=0,1,2,3,4,5

then,

a=6q

or

a=6q+1

or

a=6q+2

or

a=6q+3

or

a=6q+4

or

a=6q+5

but here,

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

⚡Hope it will help you.⚡

Answer 2

hope this will be helpful for you!

thanks for asking.