One of the more secure password managers you'll find is called 1Password. It works on all mobile platforms. This app generates complicated and very secure passwords for you...and remembers them. Its a bit complicated to set up, however, especially on Android devices. Androids don't seem to have all the capabilities that the app offers for the iPhone. Then again, the iPhone app is 18 dollars, the Android app is free.
I encourage you to check out Lastpass. It works on iPhones, Android and your computers. It is extremely easy to use. It stores web site passwords, credit card information and more behind a master password you set up. It is very secure and powerful. To get full use of all the features like automatic login, you need to buy a 12 dollar-a-year subscription.
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