| Theorems from Number Theory (MSC2010: 11)
This is a subset of the complete theorem list for the convenience of those who are looking for a particular result in number theory.
To see how this area fits into mathematics as a whole you can consult the Mathematics Subject Classification. Dave Rusin's Atlas entry is also valuable. There will inevitably be theorems which could appear here but don't and those which might be felt to belong elsewhere. I welcome comments.
Numbers in brackets are those from the complete listing.
1 (4) Euclid's Infinity of Primes
2 (5) The Chinese Remainder Theorem
3 (7) The Fundamental Theorem of Arithmetic
4 (9) Fermat's Last Theorem
5 (11) Lagrange's Four Squares Theorem
6 (13) Fermat's Little Theorem
7 (21) Brun's Theorem
8 (29) Gauss's Law of Quadratic Reciprocity
9 (32) The Green-Tao Theorem on Primes in Arithmetic Progression
10 (33) The Prime Number Theorem
11 (43) The DPRM Theorem
12 (59) Germain's Theorem
13 (78) The Three-Distance Theorem
14 (79) The Fifteen Theorem
15 (81) The Lutz-Nagell Theorem
16 (87) Lamé's Theorem
17 (91) Khinchin's Theorem on Continued Fractions
18 (115) The Hardy-Ramanujan Asymptotic Partition Formula
19 (118) Catalan's Conjecture (Mihăilescu's Theorem)
20 (127) The Lucas-Lehmer Test
21 (128) The Euclid-Euler Theorem
22 (137) Wallis's Product
23 (138) Vaughan
Pratt's Theorem
24 (151) The Short Prime Gaps Theorem
25 (153) Euler's Partition Identity
26 (156) The Lecture Hall Partition Theorem
27 (161) Quadratic Nonresidue is Zero-Knowledge Provable
28 (172) The Andrews-Garvan-Dyson Crank
29 (173) The Ramanujan Partition Congruences
30 (175) The Bungers–Lehmer Theorem on Cyclotomic Coefficients |
