MathDB

43

Part of 1978 IMO Longlists

Problems(1)

Writing k/p^2 as sum of two unit fractions

Source:

10/30/2010
If pp is a prime greater than 33, show that at least one of the numbers 3p2,4p2,⋯ ,p−2p2\frac{3}{p^2} , \frac{4}{p^2} , \cdots, \frac{p-2}{p^2} is expressible in the form 1x+1y\frac{1}{x} + \frac{1}{y}, where xx and yy are positive integers.
number theory unsolvednumber theory