modular arithmetic - How to calculate a Modulo? - Mathematics Stack Exchange
Does anyone know how to do Modulo operations in this Calculator?
Can the Mac OS calculator do modulus?
TI-84 Plus modulo
What is a modulo calculator?
How can I use the modulo operator in Python?
How does a modulo calculator work internally?
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When you see "modulo", especially if you are using a calculator, think of it as the remainder term when you do division.
Examples:
The result of 10 modulo 5 is 0 because the remainder of 10 / 5 is 0.
The result of 7 modulo 5 is 2 because the remainder of 7 / 5 is 2.
The reason your calculator says 113 modulo 120 = 113 is because 113 < 120, so it isn't doing any division.
More generally, the idea is that two numbers are congruent if they are the same modulo a given number (or modulus)
For example, as above, where
is our modulus.
Another issue is that of inverses, which is where the confusion of comes in.
We say that and
are inverses modulo
, if
, and we might write
.
For example $17\cdot 113 = 1921 = 120\cdot 16 +1 \equiv 1 \mod 12017^{-1} = 113$ modulo
.
There are ways to calculate it, modulo is remainder counting basically.
because
because
and so on, so if you want to calculate for example
you can do this, that is want to get
, take 73 and continue subtracting 7 until you no longer can.
,
etc until we get
which gives us that
in it's simplest form (any of the results along the way can technically be a).
As for what the question is simply what times 17 gives remainder 1 when divided by 120?
$113\cdot 17 = 1921 = 120\cdot 16+1$