1

Part of 2007 Putnam

Problems(2)

Source:

f

be a polynomial with positive integer coefficients. Prove that if

n

is a positive integer, then

f(n)

divides f(f(n)\plus{}1) if and only if n\equal{}1.

Putnamalgebrapolynomialfunctioncollege contests

Source:

Find all values of

\alpha

for which the curves y\equal{}\alpha x^2\plus{}\alpha x\plus{}\frac1{24} and x\equal{}\alpha y^2\plus{}\alpha y\plus{}\frac1{24} are tangent to each other.

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