Number Theory Solved Problems

1800 BCE) contains a list of "Pythagorean triples", that is, integers , presumably for actual use as a "table", for example, with a view to applications.

It is not known what these applications may have been, or whether there could have been any; Babylonian astronomy, for example, truly came into its own only later.

The number 11 is prime, for example, because its only factors are 1 and 11.

The number 12, on the other hand, is a composite (non-prime) number, because it has 5 different factors: 1, 2, 3, 4, 6, and 12.

All numbers except 0 and 1 have at least two factors: 1 and the number itself. The number 100, for example, has 9 factors: 1, 2, 4, 5, 10, 20, 25, 50, and 100.

Prime numbers are a special set of numbers that have only 2 distinct factors: 1 and the number itself.

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?

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.


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