InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Show that n2 -1 is divisible by 8, if n is an odd positive integer. |
|
Answer» Any odd positive integerncan be written in form of 4q+ 1 or 4q+ 3.Ifn= 4q+ 1, whenn2- 1 = (4q+ 1)2- 1 = 16q2+ 8q+ 1 - 1 = 8q(2q+ 1) which is divisible by 8.Ifn= 4q+ 3, whenn2- 1 = (4q+ 3)2- 1 = 16q2+ 24q+ 9 - 1 = 8(2q2+ 3q+ 1) which is divisible by 8.So, it is clear thatn2- 1 is divisible by 8, if n is an odd positive integer. |
|