I have developed some Android applications, and they don't store any personal data, but they do some calculation about some input, for example the annual salary provided by user and return to him a result to screen without saving any information. Should this application need any GDPR popup or page?
Even if your application processes personal data, but keeps it on the device, you do not need to worry about the GDPR. However the user who uses the application, processes that personal data, so (s)he must comply to the GDPR. But I assume the application is only meant to process data from the owner itself. In that case the GDPR does not apply, see Art. 2(2)(c) GDPR
This Regulation does not apply to the processing of personal data:
(c) by a natural person in the course of a purely personal or household activity;