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Re: Decomposition of a 10th degree equation
Posted:
Mar 15, 2013 10:20 AM
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On Friday, March 15, 2013 7:32:06 AM UTC-4, Deep wrote:
> Consider the following equation (1) for the given conditions.
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> x^10 + y^10 = z^10 (1)
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> Conditions: x, z are odd integers > 0 and y is non integer but x^10, y^10, z^10 are all integers each > 0
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> (1) can be decomposed as (2) and (3) where x = uv and u, v are co prime integers.
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> z^5 + y^5 = u^10 (2) z^5 - y^5 = v^10 (3)
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> It is seen that if (2) and (3) are multiplied (1) is obtained.
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> Question: Is the decomposition of (1) into (2) and (3) valid?
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> If not why not.
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> Any helpful comment will be appreciated.
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KIndly clarify. The solutions of (2) and (3) are also the solutions of (1). Given, none of (1), (2), (3) has integer solutions. That is y is a non integer in all of them. KIndly clarify the meanings of "valid), "invalid"
Thanks again.
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