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Topic: Decomposition of a 10th degree equation
Replies: 4   Last Post: Mar 16, 2013 10:17 AM

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Deep Deb

Posts: 420
Registered: 12/6/04
Decomposition of a 10th degree equation
Posted: Mar 15, 2013 7:32 AM
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Consider the following equation (1) for the given conditions.

x^10 + y^10 = z^10 (1)

Conditions: x, z are odd integers > 0 and y is non integer but x^10, y^10, z^10 are all integers each > 0

(1) can be decomposed as (2) and (3) where x = uv and u, v are co prime integers.

z^5 + y^5 = u^10 (2) z^5 - y^5 = v^10 (3)

It is seen that if (2) and (3) are multiplied (1) is obtained.

Question: Is the decomposition of (1) into (2) and (3) valid?

If not why not.
Any helpful comment will be appreciated.

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