How do you define the residual class of modulo arithmetic?

Answer

Dear Robb,

you determine the remainder class by means of a division with remainder. So suppose you want to know what the remainder class is of a number a modulo b, and dividing with remainder of a by b gives you quotient q and remainder r, then r is the searched remainder class. An example: suppose you want to know what 153 is modulo 7, then when you divide with the remainder of 153 by 7, you get q=21 and remainder r=6. The searched residual class is therefore 6 (or 153 modulo 7=6). Note that the quotient itself is not important in this one.

You can divide with remainder by means of long division, see also https://nl.wikipedia.org/wiki/Geheeltallige_deling.

Best Regards,

Joris Walraevens.