2001 JBMO Problems/Problem 1
Contents
[hide]Problem
Solve the equation in positive integers.
Solution1
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 That means and
In summary, the only solutions are
Solution2
You can also watch remainders modulo 7 which are also -1,0,1. The rest is almost identical as in solution 1.
See Also
2001 JBMO (Problems • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 | ||
All JBMO Problems and Solutions |