Difference between revisions of "User:Cxsmi"
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===The Actual Problem=== | ===The Actual Problem=== | ||
− | Find the least positive integer <math>n</math> that satisfies the following. | + | Find the least positive integer <math>n</math> that satisfies the following. The notation <math>\lfloor{x}\rfloor</math> represents the greatest integer less than or equal to <math>x</math>. |
<math>\frac{20^{23}}{n} + \frac{24^{23}}{n} = \lfloor{\frac{20^{23}}{n}+\frac{24^{23}}{n}}\rfloor \neq \lfloor{\frac{20^{23}}{n}}\rfloor + \lfloor{\frac{24^{23}}{n}}\rfloor</math> | <math>\frac{20^{23}}{n} + \frac{24^{23}}{n} = \lfloor{\frac{20^{23}}{n}+\frac{24^{23}}{n}}\rfloor \neq \lfloor{\frac{20^{23}}{n}}\rfloor + \lfloor{\frac{24^{23}}{n}}\rfloor</math> |
Revision as of 15:22, 21 January 2024
Contents
[hide]About Me
Hi! I'm just another guy who happens to enjoy math. I often pop onto the AOPS wiki and look for problems to solve, and I sometimes even write solutions for them! I've starred ⭐ a few of my favorite solutions below; please feel free to take a look at any of them. Thanks for visiting my user page, and enjoy your stay!
Solutions
AIME
AMC 8
- 2012 AMC 8 Problem 19 Solution 6 ⭐
- 2002 AMC 8 Problem 17 Solution 3
- 2007 AMC 8 Problem 20 Solution 8
- 2018 AMC 8 Problem 23 Solution 5 ⭐
- 2016 AMC 8 Problem 13 Solution 3
- 2017 AMC 8 Problem 9 Solution 2
- 2012 AMC 8 Problem 20 Solution 7
AJHSME
- 1997 AJHSME Problem 22 Solution 1
- 1985 AJHSME Problem 1 Solution 2
- 1985 AJHSME Problem 24 Solution 2 ⭐
- 1985 AJHSME Problem 2 Solution 5
AHSME
- 1950 AHSME Problem 40 Solution 2
- 1950 AHSME Problem 41 Solution 2
- 1972 AHSME Problem 16 Solution 2 ⭐
- 1950 AHSME Problem 45 Solution 3
AMC 12
Significant Problems
Here are some problems that, to me, have been significant on my math journey. This section is mainly for myself, but please please feel free to look at the problems if you're interested.
Problem
In spirit of celebrating the new year, I wrote a math problem which I thought was pretty interesting! If you'd like to, please try the problem and let me know what you think. It's written in the AIME format -- that is, the answer is an integer between and inclusive. If you're seeing this a while after the new year, it's probably because I'm too lazy to update the text here.
The Actual Problem
Find the least positive integer that satisfies the following. The notation represents the greatest integer less than or equal to .