# Why not Four?

Let n be a positive integer. Prove that 3^{2n}+1 is divisible by 2,but not by 4.

- 5 August, 2012 -
- Article, Math Problems -
- Tags : 104 problems, number theory, titu
- 0 Comments

We want to show that if

(1)

By the properties of the operation,

can be rewritten as

(2)

Furthermore, we observe that .

Because , then becomes

Therefore, is not divisible by 4. Since is clearly odd, then must be even.