valianth1 said:Homework Statement
Evaluate (16^1000 - 18^2000)(mod 17)
Homework Equations
I'm not sure how to go about doing this, but I realize it has something to do with the pattern from the last digit obtained from the 2 large numbers
The Attempt at a Solution
valianth1 said:16(mod 17) = -1 and 18(mod 17) = 1, how do I go from here?
valianth1 said:Turns out 16(mod17) is 16, so how would I go about calculating 16^1000 seeing that the exam does not permit calculators? So would the solution be 16^1000 - 1^2000? So is the solution 15? Because using the calculator returns 0 which I don't think is right
The mod of a number is the remainder after dividing that number by another number. Finding the mod of large numbers involves calculating the remainder after dividing a large number by another number.
Finding the mod of large numbers is important in many fields, including mathematics, computer science, and cryptography. It is used in algorithms and equations to solve complex problems and can also be used to ensure data integrity and security.
To find the mod of large numbers, you can use the modulo operator (%) in most programming languages. In mathematics, you can use the division algorithm or long division to find the remainder. There are also various algorithms and methods specifically designed for finding the mod of large numbers.
Applications of finding the mod of large numbers include cryptography, where it is used to ensure the security of data and communications. It is also used in computing, particularly in programming languages and algorithms that involve division. In mathematics, it is used in number theory and can help solve problems related to prime numbers and modular arithmetic.
Technically, there is no limit to the size of numbers that can be used when finding the mod. However, as the numbers get larger, the calculations required to find the mod can become more complex and time-consuming. In practical applications, there may be limitations based on computational power and the resources available.