Re: 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: [mg102455] Re: a^k+b^k+c^k = d^k+e^k+f^k, for k = 2,4, with a constraint
• From: Peter Breitfeld <phbrf at t-online.de>
• Date: Sun, 9 Aug 2009 18:21:39 -0400 (EDT)
• References: <h5m6ut\$fe5\$1@smc.vnet.net>

```TPiezas wrote:

> 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
>

You may give FindInstance a try, I asked for a,b,c not 0 to get a
non-trivial result:

gl[k_, y_] = {a^k + b^k + c^k == d^k + e^k + f^k,
a^2 + b^2 + c^2 == y^2 , a != 0, b != 0, c != 0}

FindInstance[gl[2,3],{a,b,c,d,e,f}]

Out= {{a -> -2, b -> -1, c -> -2, d -> -2, e -> -1, f -> -2}}

--
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de

```

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