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June 28th, 2019, 05:44 AM   #1
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Simplify modulus expression

Can someone tell me how to simplify this expression with modulus:

$\displaystyle (A/100) mod 10 + (A/10) mod 10 + A mod 10$

where $\displaystyle A$ is an integer, but it can also be not divisible by 100.

I tried doing this, but it doesn't work...

$\displaystyle (A/100+A/10+A)mod 10$

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June 28th, 2019, 08:22 AM   #2
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I thought 111 was the key, but it's not working out so far.

Not sure if it makes a difference, but are we taking $\displaystyle a mod b$ to be an integer (truncated mod) or allowing real numbers?
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June 28th, 2019, 11:28 AM   #3
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In this case we are takig all real numbers, so that for example $\displaystyle 6.5987 mod 2$ is congruent to $\displaystyle 0.5987$. We aren't considering truncated mod.

What's 111, you've mentioned?
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June 28th, 2019, 11:55 AM   #4
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Well, $\displaystyle (A/100) mod 10$ is the hundreds digit (plus everything after right-shifted two decimal places), $\displaystyle (A/10) mod 10$ is the tens digit, and $\displaystyle (A) mod 10$ is the ones digit.
$\displaystyle A=1325$ yields 3.25 + 2.5 + 5 = 10.75.

I thought multiplying by 111 (i.e., 100*1 + 10*1 + 1*1) either before or after the modulo might achieve the same result, but so far it doesn't seem to be working.
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June 28th, 2019, 12:14 PM   #5
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Thanks for your answer.

Can't we use the proprieties:$\displaystyle (a + b)mod c = (a mod c + b mod c) mod c$?
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June 28th, 2019, 03:20 PM   #6
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Not that I can see, because there's no modulo on the whole thing.

$\displaystyle (A*1.11) mod 10$, for example almost works, but it's usually going to be off by a multiple of ten.

$\displaystyle (1325*1.11) mod 10 = 1470.75 mod 10 = 0.75$, not 10.75.

$\displaystyle (1325 mod 1000)*1.11 = 325*1.11 = 360.75$, again not 10.75.
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June 28th, 2019, 11:20 PM   #7
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So, there is no solution, I can't do any gathtering of $\displaystyle A$ or $\displaystyle mod\,\,10$?
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June 29th, 2019, 12:56 AM   #8
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I said I can't see one. To say there isn't one, you'd have to define a form of the simplification you expect and formulate a proof that it cannot equal the original expression.

As the username says, I'm an engineer, not a mathematician.
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June 29th, 2019, 02:35 PM   #9
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Thanks DarnItJimImAnEngineer. Others?
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