Page 14: Ramanujan and Fifth Powers

New!:  Check out this author's "A Collection of Algebraic Identities" for more equal sums of like powers.

"Ramanujan and Fifth Power Identities" Ramanujan gave several identities of the form,      a1^4 + a2^4 + a3^4 = 2b1^(2k) for a positive integer k.  It turns out we can generalize this to third and fifth powers,      a1^3 + a2^3 + a3^3 + a4^3 = 2b1^(3k)      a1^5 + a2^5 + a3^5 + a4^5 + a5^5 + a6^5 = 2b1^(5k) Other quintic identities will also be given, including a sum-product in binary quadratic forms that is analogous to the ones found for third and fourth powers.

Choose your format:

Ramfifth.html

Ramfifth.pdf

See also: http://mathworld.wolfram.com/topics/Piezas.html

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This webpage was born May 5, 2006