JPanthon said:Homework Statement
Let p be a prime number.
Prove:
(a+b)^p modp = [(a^p modp) + (b^p modp)]modpHomework Equations
modular arithmetic.The Attempt at a Solution
I honestly haven't the slightest clue.
Would induction be my best bet here?
If so, when I suppose the statement is true for (k+1), n isn't always prime anymore.
I used to be a biochem major and just switched into algebra, so I'm sorry if I seem retarded, I'm just very behind! Help please!
Modular arithmetic is a branch of mathematics that deals with operations on integers, where the result of the operation is always within a fixed range. This range is called the modulus, and it is typically denoted by the symbol "mod".
Modular arithmetic can be used to prove statements involving exponents by using the properties of modular arithmetic to simplify the expressions. This is especially useful when dealing with large numbers, as it allows us to work with smaller numbers that have the same remainder when divided by the modulus.
In modular arithmetic, congruence is used to represent the relationship between two numbers that have the same remainder when divided by the modulus. On the other hand, equality is used to represent the relationship between two numbers that are exactly the same. While congruence may imply equality in some cases, they are not always the same.
Some common properties of modular arithmetic include commutativity, associativity, and distributivity. These properties allow us to manipulate the expressions in a modular arithmetic proof with exponents to simplify them and make the proof easier to understand.
Yes, modular arithmetic has many applications in various fields of science, including computer science, cryptography, and physics. It is especially useful in situations where the numbers involved are very large and need to be simplified for easier calculations.