Number Theory #
Syllabus #
File: math102-syllabus.pdf
Notes during orientation #
- No complex numbers in this class
- If we use the variable , it is assumed it is an integer
- assumes a prime number
Warm up #
Breakdown according to oldest age:
- note that 36 appears twice, since Mary needs more time to figure it out it must be this value
- When Rafael talks about his “eldest” son that means that one son is older than the rest, so the answer is 9 2 2
Important sets #
- , the set of all integers.
- , the set of all positive integers.
- all numbers that can be written as where and . So, is contained in , but is not contained in .
- is the set of all real numbers, also denoted by . is contained in , but has elements that are not in .
Primes and composites #
Any integer which is only divisible by and itself is called a prime number.
Any integer , which is not a prime, is a composite number.
Definition: The Fundamental Theorem of Arithmetic
- All composite numbers are products of primes. We call these products prime factorizations.
- Each composite number has only one prime factorization (sometimes abbreviated as pf), up to order.
Finding the prime factorization of composite numbers #
Divide by the smallest prime which goes in repeatedly. So,