2001 JBMO Problems/Problem 1
Revision as of 21:47, 11 August 2018 by Rockmanex3 (talk | contribs) (Completely FIXED the solution)
Problem
Solve the equation in positive integers.
Solution
Note that for all positive integers the value
is congruent to
modulo
Since
we find that
Thus,
and the only numbers congruent to
modulo
are
WLOG, let That means
and
Thus,
so
Now Since
we find that
Thus,
and
In summary, the only solutions are
See Also
2001 JBMO (Problems • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 | ||
All JBMO Problems and Solutions |