Difference between revisions of "User:DanielL2000"
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== Problems == | == Problems == | ||
| − | 1. Find all positive integer solutions <math> x, y, z</math> of the equation <math> 3^x \plus{} 4^y \equal{} 5^z.</math> | + | 1. Find all positive integer solutions <math> x, y, z</math> of the equation <math> 3^x \plus{} 4^y \equal{} 5^z.</math> ''(IMO Shortlist 1991)'' |
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| + | 2. Find the number of integers <math>n</math> such that <cmath>1+\left\lfloor\dfrac{100n}{101}\right\rfloor=\left\lceil\dfrac{99n}{100}\right\rceil.</cmath> ''(Harvard-MIT Math Tournament)'' | ||
Revision as of 22:25, 21 February 2014
The home of DL2000
Problems
1. Find all positive integer solutions 
of the equation $3^x \plus{} 4^y \equal{} 5^z.$ (Error compiling LaTeX. Unknown error_msg) (IMO Shortlist 1991)
2. Find the number of integers 
such that ![\[1+\left\lfloor\dfrac{100n}{101}\right\rfloor=\left\lceil\dfrac{99n}{100}\right\rceil.\]](http://latex.artofproblemsolving.com/1/2/a/12ae846f4e21c9fe5289c70c4737f00890817773.png)
(Harvard-MIT Math Tournament)
