Thread: Problem 40
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Old November 10th, 2007, 08:12 PM
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Default Problem 40
1)This problem is for the younger kids give them a chance, please. Let A,B be randomly chosen from \{ 1,2,...,2007 \} (they can be the same). What is the probability that it is possible to find two real numbers that have their product equal to A and their sum equal to B. (By the way, "real", means non-imaginary).

2)Let f(x),g(x) be continous on [0,1] so that \int_0^1 x^n f(x) dx = \int_0^1 x^n g(x) dx for all n\geq 0. Prove that f(x) = g(x). (This is a classic).
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