MathDB
Problems
Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
1998 Swedish Mathematical Competition
6
|2^{1/3} - m/n| > c/n^3
|2^{1/3} - m/n| > c/n^3
Source: 1998 Swedish Mathematical Competition p6
April 2, 2021
inequalities
algebra
Problem Statement
Show that for some
c
>
0
c > 0
c
>
0
, we have
∣
2
3
−
m
n
∣
>
c
n
3
\left|\sqrt[3]{2} - \frac{m}{n}\right | > \frac{c}{n^3}
3
2
−
n
m
>
n
3
c
for all integers
m
,
n
m, n
m
,
n
with
n
≥
1
n \ge 1
n
≥
1
.
Back to Problems
View on AoPS