Short & Sweet Math Challenge #21: Powers that be

[Paul Dale]

I'd figured out an approach to this problem. I've not implemented it on any hardware.

It is essentially a brute force approach to the problem:

For each length of polynomial (1 .. 8):

• Iterate over all polynomials for the given length that satisfy the specified constraints. That the leading coefficient is 1, the constant term is ±1 and the remaining term coefficients are from {-1, 0, 1}.
• Over all lengths there are 6560 such polynomials. If the constant term can also be 0, the count is 9840.
• Find the roots of each polynomial.
• If there is one real root > 1 and all of the remaining (possibly complex) roots have |root| < 1, then the polynomial is of the required form.