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Putnam 2001 A3

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February 26, 2012
Putnamalgebrapolynomialquadraticsquadratic formulacollege contests

Problem Statement

For each integer mm, consider the polynomial Pm(x)=x4−(2m+4)x2+(m−2)2. P_m(x)=x^4-(2m+4)x^2+(m-2)^2. For what values of mm is Pm(x)P_m(x) the product of two non-consant polynomials with integer coefficients?
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