Question

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

Answer 1

Hii friend,

Let n be the positive odd integer.

On dividing n by 6 , let Q be the Quotient and r be the remainder.

By Euclid's division lemma, we have

n = 6q + r , where r = 0,1,2,3,4,5

When r = 1

Then,

n = 6q

When r = 2

Then,

n = 6q+1

When r = 2

Then,

n = 6q+2

When r = 3

n = 6q+3

When r = 4

n = 6q +4

When r = 5

Then,

n =6q+5

Clearly when n is odd then the Value of n = (6q+1), (6q+3) and (6q+5) .


HOPE IT WILL HELP YOU.... :-)