Number theory is a subdiscipline of math which studies the properties of numbers. "Study on Number Theory" section includes basic theory and special explored section The section of basic theories is a supplement to the main part of Elementary number theory, including, Pythagoras equation, congruence theory, unitary congruence equation, quadratic congruence equation and the original root and so on, and the basic theories also make considerable improvement for the above. May this old and promising subject become a part of middle-school math teaching. The part of thematic Exploratory includes the following chapters: a concrete explanation of Fermat conjecture; the primality test for Fermat Number Fn;the application of congruence equations; the distribution of related prime numbers; primes pair of even numbers; the fundamental problems of transfinite numbers.
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