Waring's Problem & Lagrange's Four-Square Theorem

$latex \displaystyle \mathrm{num}\ = \square+\square+\square+\square &fg=000000$ Introduction We are all familiar with the problem of splitting numbers into products of primes. This process is called factorisation. The problem of expressing numbers as sums of smaller numbers has also been studied in great depth. We call such a decomposition a partition. The Indian mathematician Ramanujan proved…

Waring's Problem -- from Wolfram MathWorld

Figurate numbers

Waring's Problem -- from Wolfram MathWorld

Lagrange's four-square theorem - Wikiwand

Are there any numbers which cannot be written as a sum of three cubes or sums of four squares? If yes, then how many such numbers exist and what are they?

PDF) Quarternions and the Four Square Theorem

Analytic number theory Facts for Kids

Methods of Solving Number Theory Problems - Ellina Grigorieva - Innbundet (9783319909141) » Bokklubben

benjamin fine, gerhard rosenberger] number theory(bookos org) by Elias Vieira - Issuu

summation - Representing an Integer as a Sum of at Most $k$ Triangular Numbers - Mathematics Stack Exchange

PPT - Waring's Problem PowerPoint Presentation, free download - ID:4504701

PPT - Waring's Problem PowerPoint Presentation, free download - ID:4504701

Four Square Theorem - Quaternions, PDF, Prime Number

MathType on X: Lagrange's four-square theorem asserts that any positive whole number can be written as the sum of four squares of integers. Leave an example in the comments! #MathType #NumberTheory #math #mathematics #mathproblems #mathfacts