Inspired by Nihar

Algebra Level 5

x26+4x25+9x24+16x23+...+676x+729=0\large x^{26} + 4x^{25} + 9x^{24} + 16x^{23} + ... + 676x + 729=0

If a1a_{1}, a2a_{2}, a3a_{3}..., a25a_{25}, and a26a_{26} are the roots of the equation above whose coefficients are of the form n2n^{2}, what is the constant of the monic polynomial whose roots are 1a11-a_{1}, 1a21-a_{2}, 1a31-a_{3}, ... 1a251-a_{25}, and 1a261-a_{26}?

Kind of inspired by this problem.

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