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a^k+b^k+c^k = d^k+e^k+f^k, for k = 2,4, with a constraint

• To: mathgroup at smc.vnet.net
• Subject: [mg102426] a^k+b^k+c^k = d^k+e^k+f^k, for k = 2,4, with a constraint
• From: TPiezas <tpiezas at gmail.com>
• Date: Sun, 9 Aug 2009 06:04:24 -0400 (EDT)

Hello all,

It's easy to find small and non-trivial solns to the multi-grade eqn,

a^k+b^k+c^k = d^k+e^k+f^k, for k = 2,4.

However, I need the additional constraint that,

a^2+b^2+c^2 = y^2.

What's an efficient and _fast_ code in Mathematica to find solns to
this?  Any help will be appreciated.  Thanks.

P.S. This system came up in a certain 6-8-7 identity similar to
Ramanujan's 6-10-8.

- Titus