Trinomial decics x^10+ax+b = 0; Help with Mathematica code

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• Subject: [mg93280] Trinomial decics x^10+ax+b = 0; Help with Mathematica code
• From: tpiezas at gmail.com
• Date: Sun, 2 Nov 2008 01:57:13 -0500 (EST)

```Hello guys,

I need some help with Mathematica code.

It is easy to eliminate "n" between the two eqn:

-a + m^9 - 8m^7n + 21m^5n^2 - 20m^3n^3 + 5mn^4 = 0
-b + m^8n - 7m^6n^2 + 15m^4n^3 - 10m^2n^4 + n^5 = 0

using the Resultant[] command to find the rather simple 45-deg
polynomial in "m", call it R(m).

As Mathematica runs through integral values of {a,b}, if for some
{a,b} the poly R(m) factors, we are interested in two cases:

Case1: an irreducible decic factor
Case2: an irreducible quintic factor

What is the Mathematica code that tells us what {a,b} gives Case 1 or
Case 2?

Thanks.  :-)

Tito

```

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