Number Theory * Introduction (1/22)
... For any k > 2, are there any (non-trivial) solutions in natural numbers to the equation ak + bk = ck? If so, are there only finitely many, or are the infinitely many? This last problem is called Fermat’s Last Theorem. In general, equations in which we seek solutions in the natural numbers only are c ...
... For any k > 2, are there any (non-trivial) solutions in natural numbers to the equation ak + bk = ck? If so, are there only finitely many, or are the infinitely many? This last problem is called Fermat’s Last Theorem. In general, equations in which we seek solutions in the natural numbers only are c ...
Counting Primes (3/19)
... No one has discovered an exact formula (and no one will!). So, change the question: Given a number n, about how many primes are there between 2 and n? Let’s experiment a bit with Mathematica. We denote the exact number of primes below n by (n). The Prime Number Theorem (PNT). The number of primes be ...
... No one has discovered an exact formula (and no one will!). So, change the question: Given a number n, about how many primes are there between 2 and n? Let’s experiment a bit with Mathematica. We denote the exact number of primes below n by (n). The Prime Number Theorem (PNT). The number of primes be ...
![Primes in the Interval [2n, 3n]](http://s1.studyres.com/store/data/017368795_1-688e9118f5c89a0cb6fb7aedda33fc32-300x300.png)
