Difference between revisions of "1977 Canadian MO Problems/Problem 3"
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Revision as of 14:55, 5 July 2008
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,
.
1977 Canadian MO (Problems) | ||
Preceded by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • | Followed by Problem 4 |