 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

1. 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!

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