notation - Positive and negative integer that is congruent to 0 (mod 5) and incongruent to 0 (mod 6) - Mathematics Stack Exchange
Early 90's 5.0 mods... : Mustang
New sodium 0.5.0 is crashing my game with other mods. How can i find the one(s) which are the issues PLZ HELP
Why do we need to ask for info? Just put your logs on a paste site and paste a link here
More on reddit.comStarfield DLSS 3.5 Mod Now Available On PC, Upscaling Outshines Native Resolution
How do I calculate exponential modulo?
If the numbers at hand are not very big, you can simply solve the exponent first and then apply the modulo. Otherwise, you either need to apply some smart reasoning, a math theorem (like Fermat's little theorem or Euler's theorem), or a specialized computer algorithm that performs fast modular exponentiation.
How do I reduce exponential power in modulo?
To reduce power in exponentiation modulo, you need to apply the rules of modular arithmetic, or even some advanced math theorems, like Fermat's little theorem or one of its generalizations, e.g., Euler's theorem.
What is modular exponentiation?
Modular exponentiation means that we're calculating powers in modular arithmetic, that is, performing an operation of the form ab mod n, where a, b, and n are integers. If b is negative, modular exponentiation is linked to modular multiplication inverses.
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"$m$ is congruent to $n$ modulo $r$", typically written $$m\equiv n \pmod r,$$ means simply that $m-n$ is divisible by $r$. That is, $$r\mid (m-n).$$ One way to understand this is that you can get from $m$ to $n$ by adding or subtracting $r$ repeatedly.
This usage is different from the one in computer programming, where $\bmod$ is considered a binary operator giving the remainder when one number is divided by another.
Yes, $0 \equiv 0 \pmod 5$ and $0 \equiv 0 \pmod 6$, but the beauty of modular arithmetic are cycles. Namely, that if for example I choose 17 at random, then $17 \equiv 2 \pmod 5$ but $17 \equiv 5 \pmod 6$. Do you see why? We're not concerned with $0$ for this question. We're concerned with some positive and negative integer that yields that result. Another way to think about the question. "What is a positive integer that is divisible by 5, but not divisible by 6? Now, what is a negative integer that is divisible by 5, but not divisible by 6?"
One example is $15$. $15 \equiv 0 \pmod 5$, and $15 \equiv 3 \pmod 6$. For a negative number, we have $-15$. $-15 \equiv 0 \pmod 5$ and $-15 \equiv 3 \pmod 6$. Do you see why that works?