Name: Math 490, Fall 2012: Homework #1 Due
... Start with a right triangle with both legs having length 1. What is the length of the hypotenuse? Suppose we draw a line segment of length 1 perpendicular to the hypotenuse and then make a new triangle by drawing a line segment connecting the endpoint of the new line to the base of the original tria ...
... Start with a right triangle with both legs having length 1. What is the length of the hypotenuse? Suppose we draw a line segment of length 1 perpendicular to the hypotenuse and then make a new triangle by drawing a line segment connecting the endpoint of the new line to the base of the original tria ...
The Diophantine equation x4 ± y4 = iz2 in Gaussian
... was studied by Fermat, who proved that there exist no nontrivial solutions. Fermat proved this using the infinite descent method, proving that if a solution can be found, then there exists a smaller solution (see for example [1], Proposition 6.5.3). This was the first particular case proven of Ferma ...
... was studied by Fermat, who proved that there exist no nontrivial solutions. Fermat proved this using the infinite descent method, proving that if a solution can be found, then there exists a smaller solution (see for example [1], Proposition 6.5.3). This was the first particular case proven of Ferma ...
On three consecutive primes
... [4] Nagura, J. "On the interval containing at least one prime number." Proceedings of the Japan Academy, Series A 28 (1952), pp. 177--181. [5] Ishikawa, H. "Über die Verteilung der Primzahlen." Science Rep. Tokyo Bunrika Daigaku 2, 27-4 ...
... [4] Nagura, J. "On the interval containing at least one prime number." Proceedings of the Japan Academy, Series A 28 (1952), pp. 177--181. [5] Ishikawa, H. "Über die Verteilung der Primzahlen." Science Rep. Tokyo Bunrika Daigaku 2, 27-4 ...
x,
... Using the method of reduction of order, find another linear independent solution. 2. Using Laplace transform solve the boundary value problem y"- 2yf+ y(x) = x, ...
... Using the method of reduction of order, find another linear independent solution. 2. Using Laplace transform solve the boundary value problem y"- 2yf+ y(x) = x, ...
Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two. The cases n = 1 and n = 2 were known to have infinitely many solutions. This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by mathematicians. The theretofore unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics and prior to its proof it was in the Guinness Book of World Records for ""most difficult mathematical problems"".