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Decomposition of a 10th degree equation
Posted:
Mar 15, 2013 7:32 AM


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.



