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3 years ago

Prove that if m, d, and k are integers and d > 0, then (m + dk) mod d = m mod d.

1 answer:

6 0

From the rules of modular arithmetic, (A+B)mod C= (A)modC +(B)modC

So, (m + dk) mod d = (m) mod d+<span> (dk) mod d

clearly </span>(dk) mod d = 0, as one of the things (dk) mod d represents, is the remainder of dk, when divided by d, which is clearly 0.

Thus

(m + dk) mod d = (m) mod d+ (dk) mod d= (m) mod d+ 0=(m) mod d

(m + dk) mod d =(m) mod d

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<h3>What is an expression?</h3>

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Anna‘s age is eight years less than four times her sister's age right in expression for Anna‘s age how old is Anna if her sister is five years old

The expression for Anna's age is given below:-

Anna's age= 2T-4

Sister = 5 years

Anna= 2T -4

T is my sister's age. Then Anna's age will be calculated as:-

2(5)-4 = 10 - 4 = 6 years

Therefore, Anna's age will be equal to 6 years if her sister is five years old. The expression is Anna= 2T -4.

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