A collection of pdf books in elementary number theory:

Babai, L.: elementar number theory

Carmichael – The theory of Numbers

Joshua : elementary number theory

Hackman, P.: elementary number theory

Moser, L.: elementar number theory

Stein, W.: elementary number theory

Millersville.edu and elementary number theory

Santos, D.A.: elementar number theory

Sato, N.: elementar number theory

Sierpinski, W.: elementary number theory

Tattersall, J. – elementary number theory

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Problem collections for Olympiads:

ImoMath, Mathlinks.ro, IMO Compendium (list of corrections to second edition is available here)

Lee, H. & Vandendriessche, P. – PEN (solutions on Aops; I am actually rewriting all solutions here )

Engel, A.- Problem-solving_strategies

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More advanced books:

Everest, G. & Ward, T. – An Introduction to Number Theory

Hardy & Wright- An Introduction To The Theory Of Numbers

Mildorf, T.: a abstract perspective

Milne, J.S. – Group theory

Milne, J.S. – algebraic number theory

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Let me know if you find any problem. Have a good reading

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