Search results
Results from the WOW.Com Content Network
In the SVG file, hover over a bar to see its statistics. The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, for which n/m is again an integer (which is necessarily also a divisor of n). For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21).
In number theory, Carmichael's theorem, named after the American mathematician R. D. Carmichael, states that, for any nondegenerate Lucas sequence of the first kind U n (P, Q) with relatively prime parameters P, Q and positive discriminant, an element U n with n ≠ 1, 2, 6 has at least one prime divisor that does not divide any earlier one except the 12th Fibonacci number F(12) = U 12 (1, − ...
Divisor function d(n) up to n = 250 Prime-power factors. In number theory, a superior highly composite number is a natural number which, in a particular rigorous sense, has many divisors. Particularly, it is defined by a ratio between the number of divisors an integer has and that integer raised to some positive power.
Let be a proper variety. By definition, a (real) 1-cycle on is a formal linear combination = of irreducible, reduced and proper curves , with coefficients . Numerical equivalence of 1-cycles is defined by intersections: two 1-cycles and ′ are numerically equivalent if = ′ for every Cartier divisor on .
Mersenne primes, named after the friar Marin Mersenne, are prime numbers that can be expressed as 2 p − 1 for some positive integer p. For example, 3 is a Mersenne prime as it is a prime number and is expressible as 2 2 − 1.
In number theory, the radical of a positive integer n is defined as the product of the distinct prime numbers dividing n. Each prime factor of n occurs exactly once as a factor of this product: r a d ( n ) = ∏ p ∣ n p prime p {\displaystyle \displaystyle \mathrm {rad} (n)=\prod _{\scriptstyle p\mid n \atop p{\text{ prime}}}p}
The hypothesis that the geometric genus is positive essentially means (by the Lefschetz theorem on (1,1)-classes) that the cohomology group () contains transcendental information, and in effect Mumford's theorem implies that, despite having a purely algebraic definition, it shares transcendental information with (). Mumford's theorem has ...
A divisor on a Riemann surface C is a formal sum = of points P on C with integer coefficients. One considers a divisor as a set of constraints on meromorphic functions in the function field of C, defining () as the vector space of functions having poles only at points of D with positive coefficient, at most as bad as the coefficient indicates, and having zeros at points of D with negative ...