Problem #PRU-111815

Problems Methods Examples and counterexamples. Constructive proofs Pigeonhole principle Pigeonhole principle (other) Discrete Mathematics Algorithm Theory Theory of algorithms (other)
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Problem

Given a square trinomial f(x)=x2+ax+b. It is known that for any real x there exists a real number y such that f(y)=f(x)+y. Find the greatest possible value of a.