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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.

Numbers in brackets are those from the complete listing.

  1. Euclid's Infinity of Primes (4)
  2. The Chinese Remainder Theorem (5)
  3. The Fundamental Theorem of Arithmetic (7)
  4. Fermat's Last Theorem (9)
  5. Lagrange's Four Squares Theorem (11)
  6. Fermat's Little Theorem (13)
  7. Brun's Theorem (21)
  8. Gauss's Law of Quadratic Reciprocity (29)
  9. The Green–Tao Theorem on Primes in Arithmetic Progression (32)
  10. The Prime Number Theorem (33)
  11. The DPRM Theorem (43)
  12. Germain's Theorem (59)
  13. The Three-Distance Theorem (78)
  14. The Fifteen Theorem (79)
  15. The Lutz–Nagell Theorem (81)
  16. Lamé's Theorem (87)
  17. Khinchin's Theorem on Continued Fractions (91)
  18. The Hardy–Ramanujan Asymptotic Partition Formula (115)
  19. Catalan's Conjecture (Mihăilescu's Theorem) (118)
  20. The Lucas–Lehmer Test (127)
  21. The Euclid–Euler Theorem (128)
  22. Wallis's Product (137)
  23. Vaughan Pratt's Theorem (138)
  24. The Short Prime Gaps Theorem (151)
  25. Euler's Partition Identity (153)
  26. The Lecture Hall Partition Theorem (156)
  27. Quadratic Nonresidue is Zero-Knowledge Provable (161)
  28. The Andrews-Garvan-Dyson Crank (172)
  29. The Ramanujan Partition Congruences (173)
  30. The Bungers–Lehmer Theorem on Cyclotomic Coefficients (175)
  31. Wilson's Theorem (194)
  32. The Robin–Lagarias Theorem (197)
  33. Fermat's Two-Squares Theorem (199)
  34. The Friedlander–Iwaniec Theorem (202)
  35. Euler's Continued Fraction Correspondence (203)
  36. The Eratosthenes–Legendre Sieve (207)
  37. The Basel Problem (210)
  38. Willans' Formula (211)
  39. Faulhaber's Formula (222)
  40. Wolstenholme's Theorem (226)
  41. The Riemann Explicit Formula (232)
  42. Euler's Even Zeta Formula (238)
  43. The Large Prime Gaps Theorem (241)
  44. A Theorem of Anderson, Cameron and Preece on Groups of Units (243)
  45. Euler's Product Formula for ζ(s) (246)
  46. A Theorem about Gaussian Moats (248)
  47. Bézout's Identity (249)

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