Question regarding mod classes

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In summary, to find the smallest positive integer that satisfies the given conditions of having a remainder of 4 when divided by 12, 17, 45, or 70, one can approach the problem by writing equivalence classes or by multiplying the moduli and adding 4. The solution x=4 is the smallest positive integer that satisfies the conditions. If a different number is preferred, the next smallest integer can be found by adding the least common multiple of the moduli.
  • #1
CalculusSandwich
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Find the smallest positive integer which when divided by 12, by 17, by 45 or by 70 gives
a remainder of 4 in each case.

I know I can approach this problem by writing the equivalence classes.

x=4mod12
x=4mod17
x=4mod45 or x=4mod70

I also know I can find x by multiplying 12*17*45 + 4, but this isn't the smallest positive integer.

Can someone help me with a formula I can use?
 
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  • #2
Erm... how about the solution x=4?
It is a solution and I don't think there are any smaller positive integers that are also a solution.
 
  • #3
If you for some reason do not like the number 4, you have to add the lcm of your moduli to get the next.
 

1. What are mod classes?

Mod classes, short for modification classes, are specific classes or categories that are used to modify or extend the functionality of a software program, typically a video game. They are often created by the game's developer or by players and can add new features, characters, or gameplay mechanics to the game.

2. How do I install mod classes?

The installation process for mod classes can vary depending on the game and the method of installation. In most cases, you will need to download the mod files and then place them in a specific folder within the game's directory. Some games may also require you to use a mod manager program to install and manage mods.

3. Are mod classes safe to use?

It is generally recommended to only use mod classes from trusted sources, such as the game's official website or reputable modding communities. This can help ensure that the mods are safe and will not cause any harm to your computer or game. However, there is always a potential risk when using mods, so it is important to do your research and proceed with caution.

4. Can mod classes be used in multiplayer games?

It depends on the game and the specific mod. Some games may have restrictions on using mods in multiplayer, while others may have specific servers or communities dedicated to using mods. It is important to check the game's guidelines and any specific rules for the server you are playing on before using mods in multiplayer.

5. Do mod classes work on all platforms?

No, mod classes are typically developed for specific platforms or versions of a game. Some mods may only work on PC, while others may be compatible with consoles or mobile devices. It is important to check the mod's compatibility before attempting to use it on your platform.

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