Fermat's Last Theorem
PROJECT ABOUT FERMAT 'S LAST THEOREM
I am going to do my project in the field of number theory. Number theory, a subject with a long and rich history, has become increasingly important because of its application to computer science and cryptography. The core topics of number theory are such as divisibility, highest common factor, primes, factorization, Diophantine equations and so on, among which I chose Diophantine equations as the specific topic I would like to go deep into.
Fermat 's Last Theorem states that if n is a positive integer greater than 2, then the Diophantine equation x^n+y^n=z^n has no nontrivial solutions. Diophantine equation is an equation together with the restriction that the only solutions of the equation of interest are those belonging to a specified set, often the set of integers or the set of rational numbers. Fermat 's last theorem has its origins in the mathematics of ancient Greece; two thousand years ago Pierre de Fermat constructed the problem in the form I described above. One great mathematician after another had been humbled by Fermat 's legacy and for three hundred years no body had been able to solve it; I only had the potential to try two of them, where n=2 and 4, which I would discuss later in my project.
Fermat 's last theorem was first introduced to me by my professor in a lecture as one of the world 's unsolved mathematic problems. At that moment, as I could not understand the problem properly so I thought it was very simple. However, when I look at it now, I know why it is one of the most difficult problems in the world. The problem looks very straightforward because it based on the one piece of mathematics that everyone can remember â" Pythagoras ' theorem: In a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. [pic] This is the fundamental theorem that every innocent schoolchild is forced to learn. Now I am going to give
I am going to do my project in the field of number theory. Number theory, a subject with a long and rich history, has become increasingly important because of its application to computer science and cryptography. The core topics of number theory are such as divisibility, highest common factor, primes, factorization, Diophantine equations and so on, among which I chose Diophantine equations as the specific topic I would like to go deep into.
Fermat 's Last Theorem states that if n is a positive integer greater than 2, then the Diophantine equation x^n+y^n=z^n has no nontrivial solutions. Diophantine equation is an equation together with the restriction that the only solutions of the equation of interest are those belonging to a specified set, often the set of integers or the set of rational numbers. Fermat 's last theorem has its origins in the mathematics of ancient Greece; two thousand years ago Pierre de Fermat constructed the problem in the form I described above. One great mathematician after another had been humbled by Fermat 's legacy and for three hundred years no body had been able to solve it; I only had the potential to try two of them, where n=2 and 4, which I would discuss later in my project.
Fermat 's last theorem was first introduced to me by my professor in a lecture as one of the world 's unsolved mathematic problems. At that moment, as I could not understand the problem properly so I thought it was very simple. However, when I look at it now, I know why it is one of the most difficult problems in the world. The problem looks very straightforward because it based on the one piece of mathematics that everyone can remember â" Pythagoras ' theorem: In a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. [pic] This is the fundamental theorem that every innocent schoolchild is forced to learn. Now I am going to give
References: • Fermat 's Last Theorem, by Simon Singh. A story of a riddle that confounded the world 's greatest minds for 358 years. • [Mo69] L. J. Mordell, Diophantine Equations, Academic Press, 1969. • [HaWr89] G. H. Hardy and E. M. Wright. An Introduction to the Theory of Numbers, 4th edition, Oxford University Press, 1980. • http://www.best.com/~cgd/home/flt/flt01.htm • http://www.math.uga.edu/~ntheory/web.html • http://www.karlscalculus.org/pythtrip.html