Abstract
We investigate the problem of finding for which sets of integers a 1,…, a k either of the equations Σ i = 1 k a i α i = 0 or Π i = 1 k α i a i = 1 has a non-trivial solution in (not necessarily distinct) conjugate algebraic numbers α 1,…, α k . The problem turns out to be connected with the existence of certain latin squares having zero determinant.
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