2001 JBMO Problems/Problem 1
Revision as of 10:01, 11 August 2018 by Rockmanex3 (talk | contribs) (Solution to Problem 1 — mods are a game changer)
Problem
Solve the equation in positive integers.
Solution
Note that for all positive integers the value
is congruent to
modulo
Since
we find that
The only numbers congruent to modulo
that are also less than
are
and
With some quick checking, we find that 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 |