If n ≥ 1, let the n t h row of an infinite triangular array consist of entries , where . We develop some properties of this array, which was discovered by Vieta. In addition, we prove some irreducibility properties of the family of polynomials . These polynomials, which we call Vieta polynomials, are related to Chebychev polynomials of the first kind.
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Neville Robbins (1988) studied this question.