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A Six Degree Polynomial

The coefficients of a 6th degree polynomial P(x) are integers and its roots
are 6 different prime numbers.
There exist two integers A and B such that P(A) = 65536 and P(B) = 45441.
P(75) < 0.
Find the 6 roots.
[Explain how you got your answer. -KD]
Source: Reader Philippe Fondanaiche.

Solution

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