# help on a concept

• Mar 7th 2010, 05:52 PM
FamilyGuy34
help on a concept
every odd integer can be written as 4k+1 which I understand because you can break it down to 2(2k) + 1. But here is the part I don't get, every odd integer can also be written as 4k + 3 for an integer k.

It says this is true in the back of my book but I don't understand why?
• Mar 7th 2010, 05:56 PM
TheEmptySet
Quote:

Originally Posted by FamilyGuy34
every odd integer can be written as 4k+1 which I understand because you can break it down to 2(2k) + 1. But here is the part I don't get, every odd integer can also be written as 4k + 3 for an integer k.

It says this is true in the back of my book but I don't understand why?

Both of the above statements are false.

Quote:

every odd integer can be written as 4k+1
What about 3 $4k+1=3 \implies k=\frac{1}{2}$ and one half is not an integer.

Quote:

every odd integer can also be written as 4k + 3 for an integer k.
This is also false. 5 is an odd integer but

$4k+3=5 \implies k =\frac{1}{2}$