Monthly Archives: May 2013

Sufficient Condition to be a Polynomial?

Appropriate Level:  Real analysis. The Question:  Suppose is infinitely differentiable and that for each there is some for which the -th derivative of at equals 0.  Must be a polynomial?  

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Cyclotomic Polynomials

Appropriate Level:  Abstract Algebra The Question:  Recall that the cyclotomic polynomials are defined for so that .  Is it true that every coefficient of every cyclotomic polynomial is either 0, 1, or -1?

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