Question

Show that any positive odd
integer is in the form 6 q + 1
or 6 q + 3 or 6q + 5 where
q = Z​

Answer 1

Step-by-step explanation:

We know that any positive number can always be expressed as 6x, 6x+1, 6x+2, 6x+3, 6x+4 or 6x+5

Out of these, 6x, 6x+2, 6x+4 are even as they are clearly multiples of 2. Hence proved that any odd no. can be expressed as 6x+1, 6x+3 or 6x+5

PS: In the solution, I used 'x' instead of 'q' as in the question.

Hope it helps