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May 31st, 2010, 10:41 PM   #1
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Solvability issues

Sorry for a repost, but this question seems quite challenging. Our proff gave us this equation:

a^n + a^(n-1) + ... + a^2 + a + x = 0
Where a,x > 2 and n > 5.

Then he asks:
1) Does there exist some (n>5), such that for that n, the equation is solvable in terms of its coefficients? Or is this equation unsolvable in terms of radicals for any (n>5)?
2) If it is unsolvable for any (n>5), does that mean if you claimed a was represented in terms of radicals of the coefficients, that statement is false?
3) If it is solvable or unsolvable for some (n>5), then what significant or interesting properties of a,x,n could you tell me for when it is unsolvable or solvable? How did you reach that step of solvability and properties?
4) If it is solvable for any (n>5), then what significant or interesting properties of a,x,n could you tell me for when it is unsolvable or solvable? How did you reach that step of solvability and properties?

Question 3,4 seem vague but im guessing he's thinking of the relationship of a,n,x to each other.
Please let the answer be basic, and understandable, something a beginner in abstract algebra can understand. I hope no one has any qualms about homework assignments, thank you
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June 1st, 2010, 01:38 AM   #2
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Re: Solvability issues

Although he admits the repost, I provide a link to the original.

viewtopic.php?t=14240
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