Group

Additive Number Theory

This group gathers theorems about representing whole numbers as sums of other numbers of a restricted form, such as squares, higher powers, primes, or figurate numbers. It covers Lagrange's and Jacobi's theorems on sums of squares, Waring's problem on sums of fixed powers, Euler's pentagonal number theorem and related partition identities, and modern additive combinatorics results, including the Green-Tao and Szemeredi theorems on arithmetic progressions hidden inside the primes and other large sets of integers.

Facts

Comparison

Era Of Emergence

1742 1

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All Additive Number Theory

Additive Number Theory

14 entries

Additive Number Theory

14 entries

Branch

Topic Area

Proved

Proved By

Named After

Statement Form

1. Goldbach's Conjecture (Wikipedia)

Wikimedia FoundationOrigins section

Quote, Origins section

On 7 June 1742, the Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler (letter XLIII), in which he proposed the following conjecture:

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Additive Number Theory

All Additive Number Theory

Behrend's Theorem

Birch's Theorem

Fermat's Polygonal Number Theorem

Fermat's Theorem on Sums of Two Squares

Glaisher's Theorem

Green-Tao Theorem

Hilbert-Waring Theorem

Jacobi's Four-Square Theorem

Lagrange's Four-Square Theorem

Legendre's Three-Square Theorem

Mann's Theorem

Pentagonal Number Theorem

Szemeredi's Theorem

Thabit ibn Qurra's Theorem