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…

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?

Table 3 from Extended Lagrange's four-square theorem

Table 3 from Extended Lagrange's four-square theorem

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Lagrange's four-square theorem

5. * In the following sequence of problems, we will

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

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