MathDB

6

Part of 1998 Swedish Mathematical Competition

Problems(1)

|2^{1/3} - m/n| > c/n^3

Source: 1998 Swedish Mathematical Competition p6

4/2/2021
Show that for some c>0c > 0, we have ∣23−mn∣>cn3\left|\sqrt[3]{2} - \frac{m}{n}\right | > \frac{c}{n^3} for all integers m,nm, n with n≥1n \ge 1.
inequalitiesalgebra