496 is most notable for being a perfect number, and one of the earliest numbers to be recognized as such. As a perfect number, it is tied to the Mersenne prime 31, 25 - 1, with 24 ( 25 - 1 ) yielding 496. Also related to its being a perfect number, 496 is a harmonic divisor number, since the number of proper divisors of 496 divided by the sum of the reciprocals of its divisors, 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496, (the harmonic mean), yields an integer, 5 in this case.
A triangular number and a hexagonal number, 496 is also a centered nonagonal number and a centered 11-gonal number. Being the 31st triangular number, 496 is the smallest counterexample to the hypothesis that one more than an even indexed triangular number is a prime number. It is the largest happy number less than 500.
There is no solution to the equation φ(x) = 496, making 496 a nontotient.
E8 has real dimension 496.
Read more about this topic: 496 (number)
Other articles related to "in mathematics, mathematics":
... Range (mathematics), a set containing the output values produced by a function Interval (mathematics), also called a range, a set of real numbers ...
... Gauss referred to mathematics as "the Queen of the Sciences" ... Of course, mathematics is in this sense a field of knowledge ... Of course, the role of empirical experimentation and observation is negligible in mathematics, compared to natural sciences such as psychology, biology, or physics ...
... 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 ...
... 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 Ljubljana ... He taught and solved problems from many fields the usage of mathematics in natural and social sciences, statistics, mechanics, classical applied mathematics, discrete ...
... 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:
“The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.”
—Willard Van Orman Quine (b. 1908)
“... though mathematics may teach a man how to build a bridge, it is what the Scotch Universities call the humanities, that teach him to be civil and sweet-tempered.”
—Amelia E. Barr (18311919)