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The limit of a sequence of powers of a number greater than one diverges; in other words, the sequence grows without bound: b n → ∞ as n → ∞ when b > 1. This can be read as "b to the power of n tends to +∞ as n tends to infinity when b is greater than one". Powers of a number with absolute value less than one tend to zero: b n → 0 as ...
An abundant number whose abundance is greater than any lower number is called a highly abundant number, and one whose relative abundance (i.e. s(n)/n ) is greater than any lower number is called a superabundant number; Every integer greater than 20161 can be written as the sum of two abundant numbers. The largest even number that is not the sum ...
If 2 k + 1 is prime and k > 0, then k itself must be a power of 2, [1] so 2 k + 1 is a Fermat number; such primes are called Fermat primes. As of 2023 [update] , the only known Fermat primes are F 0 = 3 , F 1 = 5 , F 2 = 17 , F 3 = 257 , and F 4 = 65537 (sequence A019434 in the OEIS ).
A prime number is a number greater than 1 that can only be divided by… Answer: One and itself. What is the sum of the interior angles of a triangle? Answer: 180 degrees. What is the square root ...
The only known powers of 2 with all digits even are 2 1 = 2, 2 2 = 4, 2 3 = 8, 2 6 = 64 and 2 11 = 2048. [12] The first 3 powers of 2 with all but last digit odd is 2 4 = 16, 2 5 = 32 and 2 9 = 512. The next such power of 2 of form 2 n should have n of at least 6 digits.
In number theory, given a positive integer n and an integer a coprime to n, the multiplicative order of a modulo n is the smallest positive integer k such that (). [1]In other words, the multiplicative order of a modulo n is the order of a in the multiplicative group of the units in the ring of the integers modulo n.
A doubly even number is an integer that is divisible more than once by 2; it is even and its quotient by 2 is also even. The separate consideration of oddly and evenly even numbers is useful in many parts of mathematics, especially in number theory, combinatorics , coding theory (see even codes ), among others.
G(3) is at least 4 (since cubes are congruent to 0, 1 or −1 mod 9); for numbers less than 1.3 × 10 9, 1 290 740 is the last to require 6 cubes, and the number of numbers between N and 2N requiring 5 cubes drops off with increasing N at sufficient speed to have people believe that G(3) = 4; [22] the largest number now known not to be a sum of ...