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

Apr 17, 2019

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Apr 17, 2019
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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
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also liking your own comment. how low

Guest Apr 17, 2019
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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
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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.

Apr 17, 2019
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Thanks

Bxtterman  Apr 17, 2019
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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.

Apr 18, 2019