Difference between revisions of "2000 JBMO Problems/Problem 2"
(Created page with "== Solution == After rearranging we get: <math>(k-n)(k+n) = 3^n</math> Let <math>k-n = 3^a, k+n = 3^{n-a}</math> we get: <math>2n = 3^a(3^{n-2a} - 1)</math> or, <math>(2n/(...") |
(No difference)
|
Revision as of 00:12, 4 December 2018
Solution
After rearranging we get:
Let
we get: or,
Now, it is clear from above that divides . so,
If
so
But
If then increases exponentially compared to so cannot be .
Thus .
Substituting value of above we get:
or this results in only or
Thus or .