Elementary Number Theory 5th Edition

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On the Number of Primes Less Than a Given Magnitude - On the Number of Primes Less Than a Given Magnitude (or Über die Anzahl der Primzahlen unter einer gegebenen Grösse) is a seminal 8-page paper by Bernhard Riemann published in the November 1859 edition of the Monthly Reports of the Berlin Academy. Although it is the only paper he ever published on number theory, it contains ideas which influenced thousands of researchers during the late 19th century and up to the present day.

Bernoulli number - In mathematics, the Bernoulli numbers are a sequence of rational numbers with deep connections in number theory. Although easy to calculate, the values of the Bernoulli numbers have no elementary description; they are closely related to the values of the Riemann zeta function at negative integers.

Additive number theory - Additive number theory is an area of number theory that studies ways to express a determined integer as a sum of integers in a set. A famous problem in this area of number theory is Goldbach's conjecture.

Probabilistic number theory - Probabilistic number theory is a subfield of number theory, which uses explicitly probability to answer questions of number theory. One basic idea underlying it is that different prime numbers are, in some serious sense, like independent random variables.

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