Posted by
Anjali Kaur
on
Dec 06, 2021
Numbers, quantification, and numerical applications
Numbers, quantification and numerical applications, applied mathematics, class XII.
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Modulo Arithmetic
Consider the remainder when an integer is divided by another integer.
For example, if a/b, and a = bq+r
where q-quotient
r -remainder
a mod b = r
like 14 mod 5 = 4
Modulo Addition
- If a + b = c
then, a (mod n) + b (mod n) = c (mod n)
2.
3.
4.
Modular Subtraction
(A – B) mod C = (A mod C – B mod C) mod C
Congruence Modulo
Let a,b be two integers and m be a positive integer other than 1. Then ‘a’ is said to be congruent to ‘b’ modulo m, if m divides (a-b).
a = b (mod m)
For example, 123 = 21 (mod 6) why?
(123-21)/6 = 102/6 = 17.
So, yes
a = b (mod m), because m divides (a-b) completely.
Thank You!
You can check the following posts related to applied mathematics:
- Logical Reasoning – Basics
- What are functions?
- What is probability?
- Relations and functions
- Sets and Venn diagram
- What are the different types of sets?
- Set theory
Happy Learning!
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