1988 USAMO Problems/Problem 1

Revision as of 13:49, 15 May 2012 by 1=2 (talk | contribs) (Created page with "==Problem== The repeating decimal <math>0.ab\cdots k\overline{pq\cdots u}=\frac mn</math>, where <math>m</math> and <math>n</math> are relatively prime integers, and there is at ...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

The repeating decimal $0.ab\cdots k\overline{pq\cdots u}=\frac mn$, where $m$ and $n$ are relatively prime integers, and there is at least one decimal before the repeating part. Show that $n$ is divisble by 2 or 5 (or both). (For example, $0.011\overline{36}=0.01136363636\cdots=\frac 1{88}$, and 88 is divisible by 2.)

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See Also

1988 USAMO (ProblemsResources)
Preceded by
First Question
Followed by
Problem 2
1 2 3 4 5
All USAMO Problems and Solutions