It is well-known that,

D. Bailey, J. Borwein, D. Bradley gave a generalization. First define,

Obviously,

However, a little experiment with Mathematica’s *LatticeReduce* command will show there are* two* solutions for ,

where {*a, b*} are scaling variables. Adding the two together,

hence there are an infinite number of solutions. For appropriately chosen {*a,b*}, we can also eliminate one term. Thus,

For , there are now *three* solutions. Given the five terms,

then the coefficients such that their sum is equal to zero are,

Using the same approach above, we can eliminate two of the terms. One solution has an interesting number pop up,

though the appearance of *163* is probably only a coincidence. See Bailey, Borwein, Bradley’s paper for more details.

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