1977 Canadian MO Problems/Problem 3
Revision as of 23:32, 24 July 2006 by Solafidefarms (talk | contribs) (minor div flip, latex - \mid instead of a pipe)
Problem
is an integer whose representation in base
is
Find the smallest positive integer
for which
is the fourth power of an integer.
Solution
Rewriting in base
for some integer
Because
and
is prime,
Since we want to minimize
we check to see if
works.
When
Solving this quadratic,
.