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3

Part of 2001 Putnam

Problems(2)

Putnam 2001 A3

Source:

2/26/2012
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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Putnam 2001 B3

Source:

2/27/2012
For any positive integer nn, let <n> \left< n \right> denote the closest integer to n \sqrt {n} . Evaluate: ∑n=1∞2<n>+2−<n>2n \displaystyle\sum_{n=1}^{\infty} \dfrac {2^{\left< n \right>} + 2^{- \left< n \right>}}{2^n}
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