Number theory explores the fundamental properties our number system -- and if numbers aren't beautiful, we don't know what is. From primes (2, 3, 5, ...) to bases (humans like base 10 because of their fingers, while computers use base 2) to the math that fuels modern cryptography, number theory illuminates the deep connections between numbers.
You can divide 6 into equal parts of 1, 2, 3, or 6 (but not 4 or 5) because 6 is divisible by these numbers. The rules of divisibility have wide-ranging applications as an easy test for divisibility.
2, 3, 5, 7, ... The set of prime numbers is the alphabet of mathematics that allows us to communicate across the universe.
Learn how to break down numbers big and small, as proposed by the Fundamental Theorem of Arithmetic.
What is the largest number that can divide two numbers without a remainder? What is the smallest number that is divisible by two numbers without a remainder?
How would math be different if humans only had 6 fingers and 8 toes? How does a computer do math if it has no fingers to count on?
2! = 2, 3! = 3*2, 4! = 4*3*2… and 100! is a lot better than writing out 158 digits. 90! is the largest factorial that can fit in a tweet.
Is 0 an even number? Is 1 a prime number? Avoid these common misconceptions and learn the truth!
Can all numbers be written as fractions? Don't be irrational - understand some of the fundamental classifications of numbers.
Considering the remainder "modulo" an integer is a powerful, foundational tool in Number Theory. You already use in clocks and work modulo 12.
Solve integer equations, determine remainders of powers, and much more with the power of Modular Arithmetic.
Euler's theorem relate to the remainder of various powers and has applications ranging from modern cryptography to recreational problem-solving.
It might seem counterintuitive, but if you convolute these complicated things, they'll simplify in no time! Extend your understanding of the totient function by studying this class of functions.
Is there a perfect square that leaves a remainder of 7 when divided by 82? We don't need to list out all the squares, but just need to check that (7/82)=-1.
Results in number theory discovered hundreds of years ago by Fermat and Euler fuel the modern cryptography keeping your texts, emails, and other electronic data safe.
What amounts of money can you make with only $5 and $7 bills? Can you make $23 with those 2 types of bills?
The Pythagorean Theorem is one of the most famous quadratic diophantine equations, which are equations with squared variables solved over the integers. How many solutions can you find?
We have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain.