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However, amicable numbers where the two members have different smallest prime factors do exist: there are seven such pairs known. [8] Also, every known pair shares at least one common prime factor. It is not known whether a pair of coprime amicable numbers exists, though if any does, the product of the two must be greater than 10 65.
m is a divisor of n (also called m divides n, or n is divisible by m) if all prime factors of m have at least the same multiplicity in n. The divisors of n are all products of some or all prime factors of n (including the empty product 1 of no prime factors). The number of divisors can be computed by increasing all multiplicities by 1 and then ...
There are exactly 220 different ways of partitioning 64 = 8 2 into a sum of square numbers. [6] It is a tetrahedral number, the sum of the first ten triangular numbers, [7] and a dodecahedral number. [8] If all of the diagonals of a regular decagon are drawn, the resulting figure will have exactly 220 regions. [9]
Two numbers with the same "abundancy" form a friendly pair; ... 88: 180: 45/22 89: 90: 90/89 ... at least one of the prime factors must be congruent to 1 modulo 3 and ...
Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem. To factorize a small integer n using mental or pen-and-paper arithmetic, the simplest method is trial division : checking if the number is divisible by prime numbers 2 ...
88 is: a refactorable number. [1] a primitive semiperfect number. [2] an untouchable number. [3] a hexadecagonal number. [4] an Erdős–Woods number, since it is possible to find sequences of 88 consecutive integers such that each inner member shares a factor with either the first or the last member. [5]
d() is the number of positive divisors of n, including 1 and n itself; σ() is the sum of the positive divisors of n, including 1 and n itselfs() is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n
The polynomial x 2 + cx + d, where a + b = c and ab = d, can be factorized into (x + a)(x + b).. In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.