User:DanielL2000: Difference between revisions
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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)'' | 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)'' | ||
3. Compute <cmath>\sum_{a_1=0}^\infty\sum_{a_2=0}^\infty\cdots\sum_{a_7=0}^\infty\dfrac{a_1+a_2+\cdots+a_7}{3^{a_1+a_2+\cdots+a_7}}.</cmath> ''(Harvard-MIT Math Tournament)'' | |||
== Online Math Circle == | == Online Math Circle == | ||
Revision as of 22:31, 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)
3. Compute ![\[\sum_{a_1=0}^\infty\sum_{a_2=0}^\infty\cdots\sum_{a_7=0}^\infty\dfrac{a_1+a_2+\cdots+a_7}{3^{a_1+a_2+\cdots+a_7}}.\]](http://latex.artofproblemsolving.com/9/3/3/933e7f1dfd766f8b0e55bb5bb9d3672ff92c0509.png)
(Harvard-MIT Math Tournament)
Online Math Circle
Go to the OMC or Online Math Circle at:
newyorkmathcircle.weebly.com
