5

Part of 1988 Swedish Mathematical Competition

Problems(1)

7- m^2/n^2 >= a/n^2 if m/n < \sqrt7

Source: 1988 Swedish Mathematical Competition p5

Show that there exists a constant

7-\frac{m^2}{n^2} \ge \frac{a}{n^2} .

such that, for any positive integers

m

n

\frac{m}{n} < \sqrt7

7-\frac{m^2}{n^2} \ge \frac{a}{n^2} .

inequalitiesalgebra