Find all 6-digit multiples of 22 of the form $5d5,\!22e$ where $d$ and $e$ are digits. What is the maximum value of $d$?

Guest Apr 17, 2019

#1**+5 **

AoPS I assume? Or some online class for math? My tips for you. These classes are expensive, and please try to do your homework and at least try to solve the problems before you ask here. If you did indeed attempt to solve these problems, please show your steps to solve. Furthermore, your effort on the post is super minimal, and you don't even format it correctly. At least take the format out of LaTeX and into readable form before you post. We are here to **help **you learn, not provide answers. If you really don't want to learn at your class/course, please just don't waste your time or sign up for it. Just a message and reminder from me.

Bxtterman Apr 17, 2019

#2**-1 **

Actually no, i was talking to my friends we created this question and decided to find out how different people solved the question. Its in latex form because thats the only way my friend know how to type math on a computer. Sorry if it was similar to one of those classes you were talking about.

Guest Apr 17, 2019

edited by
Guest
Apr 17, 2019

edited by Guest Apr 17, 2019

edited by Guest Apr 17, 2019

#4**+2 **

If LaTeX is the only way someone can type on a computer, I find that very weird. Additionally, you should be able to convert it into somewhat readable form. Also, there is a LaTeX function in the Web2.0Calc editor. I don't want to argue about this, just wanted to let you know that you should create a better story next time. Thanks.

Bxtterman
Apr 17, 2019

#5**+1 **

To me it does not make sense that you created this question yourself.

If that were the case why would you not present it in a readable format.

Melody Apr 17, 2019

#7**+1 **

**Q: Find all 6-digit multiples of 22 of the form 5d522e where d and e are digits. What's the maximum value of d?**

5d522e is divisible by 22 <=> 5d522e is divisible by 2 and also divisible by 11.

e = {0,2,4,6,8}.

5 + 5 + 2 - d - 2 - e is divisible by 11.

\(14-d-e\equiv 0 \pmod {11}\\ d+e\equiv 3 \pmod{11}\\ (d,e) = (3,0), (1,2),(8,6),(6,8)\)

The required multiples of 22 are 535220, 515222, 585226, 565228.

Maximum value of d is 8.

MaxWong Apr 18, 2019