Number Theory Solved Problems

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A Couple Of Simple Number Theory Problems And Solutions Many basic number theory problems relate to factoring.

Following are a couple of examples: Problem: You have a quantity of cookies.

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Prove that if $2^n-1$ is a Mersenne prime number, then \[N=2^(2^n-1)\] is a perfect number.

On the other hand, prove that every even perfect number $N$ can be written as $N=2^(2^n-1)$ for some Mersenne prime number ^n-1$.For further information, including about cookie settings, please read our Cookie Policy .By continuing to use this site, you consent to the use of cookies.Number Theory Examples The following are a few of the topics a course on number theory would likely address, along with a few examples of each.Factors are two whole numbers that, when multiplied together, equal a third number.Applications Of Number Theory One of the most well-known applications of number theory is cryptography, particularly online.Modern cryptography depends on prime factorization of extremely large numbers.A Brief Introduction To Number Theory Number theory is the branch of mathematics that studies integers, which are all the whole numbers on either side of the number line.Number theory looks at specific properties of integers and seeks patterns in the ways different types of numbers are distributed or related to each other.Solution: The answer is 12 because 2, 3, and 4 are all factors of 12, and 12 is the lowest common multiple of those numbers.Problem: Which of the following numbers can not be divided into any smaller equal groups: 5106, 5281, or 5751?

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