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