Tag Info

• 523

Closed form roots for polynomial $x^9 + ax^6 + bx^5 + cx^3 + d = 0$

There is no way to transform your first polynomial to the special shape of the second polynomial while preserving its Galois group. The Galois group of the second polynomial is solvable, but for ...
• 16.2k

Stothers-Mason theorem

Look up Belyi maps. See, for instance, the third page of Granville and Tucker’s survey paper on the $abc$ conjecture: It's as easy as $abc$.
• 42.5k
Accepted

• 78.5k
1 vote
Accepted

Determinant of a certain Vandermonde matrix

In Appendix B of https://arxiv.org/abs/2103.10776 (J. Phys. A: Math. Theor. 54, 375201 (2021)), I derived a transformation of the block Vandermonde determinant above to a Hankel matrix, which in my ...
• 548
1 vote

Is it possible to solve for y in this equation?

Yes, it is. In fact, this is a trinomial equation. A closed form expression can be obtained using confluent Fox-Wright Function $\ _1\Psi_1^*(\zeta)$. See here A linearly convergent series can be ...
• 1,465
Accepted

A statement on complex polynomials

The conjecture is easily seen to be true for $n<3$. We give a counterexample for $n=3$. Let $p_i = z^2 - \omega_i$ where the $\omega_i$ are the cube roots of unity. These are linearly dependent ...
• 72.3k