Stage 3 Introductory Number Theory

Introductory Number Theory:
Gauss once said "mathematics is the queen of sciences and number theory the queen of mathematics." G..H. Hardy once said in A Mathematician's Apology that, "If the theory of numbers could be employed for any practical and obviously honourable purpose, if it could be turned directly to the furtherance of human happiness or the relief of human suffering, as physiology and even chemistry can, then surely neither Gauss nor any other mathematician would have been so foolish as to decry or regret such applications. But science works for evil as well as for good (and particularly, of course, in time of war); and both Gauss and less mathematicians may be justified in rejoicing that there is one science at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean." He wrote it on November 1940. It turned out coding theory, where algebra and number theory are applied, played a key role in the World War II.