I'm a user of an iPhone 4 with iOS 7.1.2.
When I want download an app, it tells me it need to update to iOS 8.4, but it's not supported for the iPhone 4!
Is this only a requirement for specific apps or it is a bug?
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If you open the App Store page for an app and scroll to the bottom, there's a section titled "Compatibility" that will tell you what the minimum version of iOS is that the app requires.
(This is not a screenshot of the OP's problem app, but rather The Infinite Arcade, which was the first app I saw.)