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Let K be the set of polynomials of the form

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

where c 1 , c 2 , . . . , c n − 1 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?


The answer is 528.

Wu Zhou by Wu Zhou , 59, Singapore

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1 solution

Michael Tong
Jan 25, 2014

This is problem 25 from the 2013 AMC 12B. An excellent solution can be found here

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