# Thread: Modulo exercice

1. ## Modulo exercice

Hey again !

I know it is pretty simple but i dont seem to prove it.
If a=bmodk and c=dmodk then why a-c=(b-d)modk

2. ## Re: Modulo exercice

Originally Posted by grainofsand
Hey again !

I know it is pretty simple but i dont seem to prove it.
If a=bmodk and c=dmodk then why a-c=(b-d)modk
$a=k \cdot n +b \land c = k \cdot m+d \Rightarrow a-c = k \cdot(n-m)+(b-d) \Rightarrow$

$\Rightarrow a-c \equiv b-d \pmod k$

3. ## Re: Modulo exercice

thank you so much !
The text contains a mathematical question about proving a property of modulo arithmetic, and an answer that provides a proof for the question.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Thread: Modulo exercice

1. ## Modulo exercice

Hey again !

I know it is pretty simple but i dont seem to prove it.
If a=bmodk and c=dmodk then why a-c=(b-d)modk

2. ## Re: Modulo exercice

Originally Posted by grainofsand
Hey again !

I know it is pretty simple but i dont seem to prove it.
If a=bmodk and c=dmodk then why a-c=(b-d)modk
$a=k \cdot n +b \land c = k \cdot m+d \Rightarrow a-c = k \cdot(n-m)+(b-d) \Rightarrow$

$\Rightarrow a-c \equiv b-d \pmod k$

3. ## Re: Modulo exercice

thank you so much !
user
The text contains a mathematical question about proving a property of modulo arithmetic, and an answer that provides a proof for the question.

TYPE: SINGLE_QUESTION_WITH_ANSWER