Question

show that any positive odd integer is of the form 6 Q + 1 or 6q + 3 or 6 q + 5 where Q is some integer

Answer 1

Heya !!!


Let N be a given positive odd Integer.


On dividing N by 6 , Let Q be the Quotient and R be the Remainder.


Then , By Euclid's division lemma, we have


N = 6Q + R , where R = 0,1,2,3,4,5


Therefore,

N = 6Q , (6Q+1) , (6Q+2) , (6Q +3) ,(6Q+4) , (6Q+5).

N = 6Q , (6Q+2) , (6Q+4) are even values of N.

Thus,

When N is odd , it is in the form of (6Q+1) , (6Q+3) , (6Q+5) for some integer Q.



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