Question

Show that every positive odd integer is of the form (6m + 1) or (6m + 3) or (6m + 5) for some integer m.​

Answer 1

HEY MATE...

HERE IS YOUR ANSWER...

Dividend = divisor × Quotient + remainder

n = 6m + r. Where r = 0,1,2,3,4,5

n = 6m +0 = 6m [r = 0]

n = 6m +1 = 6m +1 [r = 1]

n = 6m +2 = 6m +2 [r =2]

n = 6m +3 = 6m +3 [r = 3]

n = 6m +4 = 6m + 4 [r = 4]

n = 6m +5 = 6m +5 [r = 5]

n = 6m, (6m +2),(6m+4 ) are even value of n.

Therefore..

When n is odd, it is in the form of (6m+1),(6m+3), (6m+3)for some integer m..

HOPE IT MAY HELPS YOU:)