You are in luck. There is a untethered jailbreak solution for your device.

The tools are listed below.

- How to Jailbreak 4.3.1 with JailbreakMe 3.0 (Windows) (Mac)

- How to Jailbreak iOS 4.3.1 with Redsn0w 0.9.6rc15 (Windows) (Mac)

- How to Jailbreak iOS 4.3.1 with Sn0wbreeze 2.6.1 (Windows)* preserves baseband

- How to Jailbreak iOS 4.3.1 with Redsn0w 0.9.6rc14 (Windows) (Mac)

- How to Jailbreak iOS 4.3.1 with Redsn0w 0.9.6rc13 (Windows) (Mac)

- How to Jailbreak iOS 4.3.1 with Sn0wbreeze 2.5.1 (Windows)* preserves baseband

- How to Jailbreak iOS 4.3.1 with Redsn0w 0.9.6rc12 (Windows) (Mac)

- How to Jailbreak iOS 4.3.1 with Redsn0w 0.9.6rc11 (Windows) (Mac)

- How to Jailbreak iOS 4.3.1 with Pwnage Tool 4.3 (Mac)* preserves baseband

- How to Jailbreak iOS 4.3.1 with Redsn0w 0.9.6rc10 (Windows) (Mac)

- How to Jailbreak iOS 4.3.1 with Redsn0w 0.9.6rc09 (Windows) (Mac)