Euclid 2019/Problem 5

Problem

(a) Determine the two pairs of positive integers $(a,b)$ with $a<b$ that satisfy the equation $\sqrt a+\sqrt b=\sqrt (50)$ .

(b) Consider the system of equations: $c+d=2000$ and $\frac{c}{d}=k$ . Determine the number of integers $k$ with $k\leq0$ for which there is at least one pair of integers $(c,d)$ that is a solution to the system.

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Euclid 2019/Problem 5

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