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I have:

$F(x) + G(x) = 1 + F(x)*M,$

$G(x) = T_{1}(x) + T_{2}(x) + ... + T_{N}(x)$

$F(x )x^{a_{i}} = T_{i}(x) \times C_{i}(x) + \sum_{j \leq N} T_{j}(x) \times P_{ji}(x)$

In which $M, N, a_{i}, C_{i}(x), P_{ji}(x)$ are known consts or polynomials. How can I represent $F(x)$ or $G(x)$ in form of these known factors?

UPDATE: Degree of $C_{i}, P_{ji}$ are smaller than $a_{i}$

Thank you,

share|improve this question
    
What are $T_i(x)$? Also known? If so, don't you already have formulas for $F$ and $G$ from the first two equations? –  user7530 Sep 12 '13 at 11:48
    
No, we dont know $T_{i}(x)$ :( –  Loi.Luu Sep 12 '13 at 11:55
    
Anything known about the degrees of $C_i$ and $P_{ji}$? –  user7530 Sep 12 '13 at 12:02
    
Degree of $C_{i}, P_{ji}$ are smaller than $a_{i}$ –  Loi.Luu Sep 12 '13 at 12:05
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