MathDB

B3

Part of 1982 Putnam

Problems(1)

probability c+d square, find limit

Source: Putnam 1982 B3

10/1/2021
Let pnp_n be the probability that c+dc+d is a perfect square when the integers cc and dd are selected independently at random from the set {1,2,…,n}\{1,2,\ldots,n\}. Show that lim⁡n→∞pnn\lim_{n\to\infty}p_n\sqrt n exists and express this limit in the form r(s−t)r(\sqrt s-t), where ss and tt are integers and rr is a rational number.
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