Proving with Congruence of intergers

  • Thread starter doggie_Walkes
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In summary, proving with congruence of integers involves showing that two integers have the same remainder when divided by a given integer. It is important for understanding mathematical relationships and has practical applications in fields such as cryptography and computer science. However, it has limitations and may not be the most efficient method of proof in certain situations.
  • #1
doggie_Walkes
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It just how do i prove that

b^3 +b^2 +1 does not divide by 5


Im thinking this way,
cause i know that b^3 +b^2 +1 is not congruent to 0(mod5)

therefore we use contradition to prove it. I am just not sure how to use contradition? or maybe I am looking at this in a completely bad light? maybe there is another method?
 
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  • #2
This can be worked out by considering all the cases from 0 to 4 mod 5.
 
  • #3
Double posted.
 

1. What does it mean to prove with congruence of integers?

Congruence of integers is a mathematical concept that refers to two integers having the same remainder when divided by a given integer. Proving with congruence of integers involves showing that two integers are congruent to each other when divided by a given integer.

2. Why is proving with congruence of integers important?

Proving with congruence of integers is important because it allows us to show the relationship between different integers and their remainders when divided by a given integer. This can be useful in solving mathematical problems and understanding number patterns.

3. How is proving with congruence of integers different from other methods of proof?

Proving with congruence of integers is different from other methods of proof because it is specifically used for proving the congruence of integers. Other methods of proof, such as direct proof or mathematical induction, may be used to prove other types of mathematical relationships.

4. What are some common applications of proving with congruence of integers?

Proving with congruence of integers has many practical applications in fields such as cryptography, computer science, and number theory. It can also be useful in solving problems involving divisibility and modular arithmetic.

5. Are there any limitations to proving with congruence of integers?

While proving with congruence of integers is a useful tool in mathematics, it does have some limitations. It is not applicable to all types of mathematical relationships and may not be the most efficient method of proof in certain situations. Additionally, it only applies to integers and not all types of numbers.

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