MathDB

5

Part of 2001 Putnam

Problems(2)

Putnam 2001 A5

Source:

2/26/2012
Prove that there are unique positive integers aa, nn such that an+1−(a+1)n=2001a^{n+1}-(a+1)^n=2001.
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Putnam 2001 B5

Source:

2/27/2012
Let aa and bb be real numbers in the interval (0,12)\left(0,\tfrac{1}{2}\right), and let gg be a continuous real-valued function such that g(g(x))=ag(x)+bxg(g(x))=ag(x)+bx for all real xx. Prove that g(x)=cxg(x)=cx for some constant cc.
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