User:Cxsmi

Revision as of 16:22, 21 January 2024 by Cxsmi (talk | contribs) (The Actual Problem)

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

  1. 1987 AIME Problem 11 Solution 3 ⭐
  2. 2012 AIME I Problem 2 Solution 3 ⭐

AMC 8

  1. 2012 AMC 8 Problem 19 Solution 6 ⭐
  2. 2002 AMC 8 Problem 17 Solution 3
  3. 2007 AMC 8 Problem 20 Solution 8
  4. 2018 AMC 8 Problem 23 Solution 5 ⭐
  5. 2016 AMC 8 Problem 13 Solution 3
  6. 2017 AMC 8 Problem 9 Solution 2
  7. 2012 AMC 8 Problem 20 Solution 7

AJHSME

  1. 1997 AJHSME Problem 22 Solution 1
  2. 1985 AJHSME Problem 1 Solution 2
  3. 1985 AJHSME Problem 24 Solution 2 ⭐
  4. 1985 AJHSME Problem 2 Solution 5

AHSME

  1. 1950 AHSME Problem 40 Solution 2
  2. 1950 AHSME Problem 41 Solution 2
  3. 1972 AHSME Problem 16 Solution 2 ⭐
  4. 1950 AHSME Problem 45 Solution 3

AMC 12

  1. 2021 AMC 12B Problem 12 Solution 6⭐

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.

  1. 2017 AMC 10A Problem 19 - First AMC 10 Solution of Difficulty 2 or Higher
  1. 2007 AMC 8 Problem 25 - First AMC 8 Final Five Solution
  1. 1984 AIME Problem 1 - First AIME Solution
  1. 2005 AMC 12B Problem 16 - First AMC 12 Solution of Difficulty 2.5 or Higher
  1. 2016 AMC 10A Problem 21 - First AMC 10 Final Five Solution
  1. 1987 AIME Problem 11 - First AIME Solution of Difficulty 4 or Higher
  1. 2017 AMC 12A Problem 23 - First AMC 12 Final Five Solution

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 $1$ and $999$ 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 $n$ that satisfies the following. The notation $\lfloor{x}\rfloor$ represents the greatest integer less than or equal to $x$.

$\frac{20^{23}}{n} + \frac{24^{23}}{n} = \lfloor{\frac{20^{23}}{n}+\frac{24^{23}}{n}}\rfloor \neq \lfloor{\frac{20^{23}}{n}}\rfloor + \lfloor{\frac{24^{23}}{n}}\rfloor$