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…

Lagrange's four-square theorem - Wikipedia

Lagrange's four-square theorem, polynomials, diophantine equations, prime numbers

Lagrange's four-square theorem - Wikipedia

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PDF) Lagrange's four squares theorem with one prime and three almost-prime variables

WARING'S PROBLEM FROM THE STANDPOINT OF THE COGNITIVE INTERACTIVE COMPUTER GRAPHICS

PDF) Extended Lagrange's four-square theorem

Waring's Problem -- from Wolfram MathWorld

SOLVED: Theorem 8.35 (Lagrange's Four-Square Theorem) then n can be expressed as the sum If n is a number; of four squares: natural lattice A in 4-space is a set of the

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?

Lagrange's four-square theorem

Waring's Problem -- from Wolfram MathWorld

Waring's Problem -- from Wolfram MathWorld

Lagrange's Four-Square Theorem, PDF, Number Theory