# Størmer's Theorem - Generalizations and Applications - in Mathematics

In Mathematics

Chein (1976) used Størmer's method to prove Catalan's conjecture on the nonexistence of consecutive perfect powers (other than 8,9) in the case where one of the two powers is a square.

Mabkhout (1993) proved that every number x4 + 1, for x > 3, has a prime factor greater than or equal to 137. Størmer's theorem is an important part of his proof, in which he reduces the problem to the solution of 128 Pell equations.

Several authors have extended Størmer's work by providing methods for listing the solutions to more general diophantine equations, or by providing more general divisibility criteria for the solutions to Pell equations.

### Other articles related to "mathematics, in mathematics":

Mathematics As Science
... Gauss referred to mathematics as "the Queen of the Sciences" ... Of course, mathematics is in this sense a field of knowledge ... and observation is negligible in mathematics, compared to natural sciences such as psychology, biology, or physics ...
Egon Zakrajšek
... He graduated from technical mathematics at the Department of mathematics and physics of then Faculty for natural sciences and technology (FNT) of the University of ... solved problems from many fields the usage of mathematics in natural and social sciences, statistics, mechanics, classical applied mathematics, discrete mathematics, graph and network theory, linear ...
Range - Mathematics, Science, and Technology - In Mathematics
... Range (mathematics), a set containing the output values produced by a function Interval (mathematics), also called a range, a set of real numbers that includes all numbers between any two numbers in the set ...
Foundations Of Mathematics - Foundational Crisis - Philosophical Views - Logicism
... Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all ...
Otto Toeplitz - Life and Work
... Toeplitz's father and grandfather were mathematics teachers ... Toeplitz studied mathematics in the University of Breslau and was awarded a doctorate in algebraic geometry in 1905 ... Mathematics faculty included David Hilbert, Felix Klein, and Hermann Minkowski ...

### Famous quotes containing the word mathematics:

Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.
Simone Weil (1909–1943)

It is a monstrous thing to force a child to learn Latin or Greek or mathematics on the ground that they are an indispensable gymnastic for the mental powers. It would be monstrous even if it were true.
George Bernard Shaw (1856–1950)