A cool name

Level pending

Let K be the set of polynomials of the form

P(R)=\(R^{n}\)+\(c_{n-1}\)\(R^{n-1}\)+...+\(c_{2}R^{2}\)+\(c_{1}R\)+50,

where \( c_{1},c_{2},..., c_{n-1}\) are integers and P(R) has distinct roots of the form a+ib with a and b integers. How many polynomials are in K?

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