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In mathematics. There is no answer to the equation φ ( x) = 118, making 118 a nontotient. [1] Four expressions for 118 as the sum of three positive integers have the same product: 14 × 50 × 54 = 15 × 40 × 63 = 18 × 30 × 70 = 21 × 25 × 72 = 37800. 118 is the smallest number that can be expressed as four sums with the same product in ...
The first solution with no prime number is the fourth which appears at X + Y ≤ 2522 or higher with values X = 16 = 2·2·2·2 and Y = 111 = 3·37. If the condition Y > X > 1 is changed to Y > X > 2, there is a unique solution for thresholds X + Y ≤ t for 124 < t < 5045, after which there are multiple solutions. At 124 and below, there are ...
n ! {\displaystyle n!} In mathematics, the factorial of a non-negative integer , denoted by , is the product of all positive integers less than or equal to . The factorial of also equals the product of with the next smaller factorial: For example, The value of 0! is 1, according to the convention for an empty product.
In mathematics, an operator or transform is a function from one space of functions to another. Operators occur commonly in engineering, physics and mathematics. Many are integral operators and differential operators . In the following L is an operator. which takes a function ∈ to another function [] ∈ .
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, it is possible to expand the polynomial (x + y) n into a sum involving terms of the form ax b y c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending ...
The multiplicative inverse x ≡ a −1 (mod m) may be efficiently computed by solving Bézout's equation a x + m y = 1 for x, y, by using the Extended Euclidean algorithm. In particular, if p is a prime number, then a is coprime with p for every a such that 0 < a < p ; thus a multiplicative inverse exists for all a that is not congruent to ...
In real analysis and approximation theory, the Kolmogorov–Arnold representation theorem (or superposition theorem) states that every multivariate continuous function can be represented as a superposition of the two-argument addition of continuous functions of one variable. It solved a more constrained form of Hilbert's thirteenth problem, so ...
Mathematics. 16 is the ninth composite number, and a square number: 4 2 = 4 × 4 (the first non-unitary fourth-power prime of the form p4 ). It is the smallest number with exactly five divisors, its proper divisors being 1, 2, 4 and 8 . Sixteen is the only integer that equals mn and nm, for some unequal integers m and n ( , , or vice versa). [1]