# Tagged Questions

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### what is the logic behind the 'UPC -A' check digit?

In UPC-A barcode symbology, the 12th digit is known as check digit and it is used by the scanner to determine if it scanned the number correctly or not. ...
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### Solving system of quadratic congruences

If you have a system ex: $ab \equiv 1 \mod 9$ $ab \equiv 3 \mod 10$ $ab \equiv 10 \mod 11$ $ab \equiv 7 \mod 12$ is there a way to determine integers $a$ and $b$?
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### clarification on binary and decimal representations of integers

This is from the book: Elementary number theory, David M. Burton, page 69. Given an integer $b>1$, any positive integer $N$ can be written uniquely in terms of powers of $b$ as ...
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### The Mystery of the Número Cabalístico

I recently ran into an interesting type of number that people from where I was born like to refer to as números cabalísticos. They are supposedly "magic" kinds of numbers that possess mystical ...
### Sum of $2$ two-digits numbers
$X$ and $Y$ are two-digit numbers. If $Y=2X+2$ and $Y=2X$ in decimal and octal system respectively, and unit digits of $X$ and $Y$ are $5$ and $2$ respectively, then how to find $X+Y$ in ...
### General approach for problem for finding sum from $1$ to $N$ when all $a$'s are replaced by $b$'s
The problem is: Find the sum of all the numbers from $1$ to $100$ when all the $6$'s are replaced by $9$'s. I need some ideas on how to approach this kind of problems? Please explain your ideas, ...