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

Waring's Problem -- from Wolfram MathWorld

Additive problems with almost prime squares

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

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Lagrange's four-square theorem - Wikipedia

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Waring's Problem -- from Wolfram MathWorld