Is There a Solution for Modulus with 3 Equations?

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In summary, the conversation discusses a problem involving finding the value of x without dealing with a large number, given the equations n == a mod(m) and m == b mod(r). The speaker mentions finding a and b, and considers using the Chinese Remainder Theorem but determines it is not applicable in this case. The solution is to find x given the equations x == a mod(m) and x == b mod(r).
  • #1
coolul007
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I am wondering if there is a way to solve the following:

n == a mod(m)

m == b mod(r)

n == x mod(r), I need to know x, without dealing with a gigantic number(n),

I can find a and b, as I chose m to give me predictable results.

I appreciate any insight...
 
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  • #2
Sounds like a Chinese Remainder Theorem problem. Check out the concept online or in any book on number theory.
 
  • #3
It doesn' seem to be Chinese Remainder...I've looked into that. If it was Chinese Remainder it would be solving for a number with known mods, I know the number but need the missing mod.

x == a mod(m)
x == b mod(r)
 
  • #4
Ahhh, I see. Well, never mind then!
 

FAQ: Is There a Solution for Modulus with 3 Equations?

What is modulus in mathematics?

Modulus, also known as the absolute value, is a mathematical operation that determines the distance of a number from zero. It is represented by two vertical bars, and is always positive.

How is modulus calculated?

To calculate the modulus of a number, simply remove the negative sign (if present) and keep the number as a positive value. For example, the modulus of -5 is 5.

What is the purpose of using modulus with equations?

Modulus can be used in equations to ensure that the result is always positive. This is particularly useful when dealing with absolute values or distances.

Can modulus be used with variables?

Yes, modulus can be used with variables in equations. For example, if x = -3, then the modulus of x would be 3.

How is modulus used in real-life applications?

Modulus is used in various real-life applications, such as measuring distances, calculating speed and acceleration, and determining the magnitude of a vector in physics. It is also commonly used in computer programming to determine the remainder of a division operation.

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