olymmath

Putnam 1999 A1

  • Session A

Find polynomials f(x)f(x),g(x)g(x), and h(x)h(x), if they exist, such that for all xx, ∣f(x)∣−∣g(x)∣+h(x)={−1if x<−13x+2if −1≤x≤0−2x+2if x>0.|f(x)|-|g(x)|+h(x) = \begin{cases} -1 & \text{if $x<-1$} \\ 3x+2 & \text{if $-1 \leq x \leq 0$} \\ -2x+2 & \text{if $x>0$.} \end{cases}

Curated text Kedlaya Putnam archive. Quoted with source.

Solutions

Human solution Solution 1 by Manjul Bhargava, Kiran Kedlaya and Lenny Ng

The terms of the source let olymmath link to this solution but not copy it. Read the solution (Kedlaya Putnam archive).

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