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then A and B are arithmetic progressions with the same difference. This illustrates the structures that are often studied in additive combinatorics: the combinatorial structure of A + B as compared to the algebraic structure of arithmetic progressions.
The question is whether knowing the warden's answer changes the prisoner's chances of being pardoned. This problem is equivalent to the Monty Hall problem; the prisoner asking the question still has a 1 / 3 chance of being pardoned but his unnamed colleague has a 2 / 3 chance.
This is widely used in modular arithmetic, because this allows reducing modular exponentiation with large exponents to exponents smaller than n. Euler's theorem is used with n not prime in public-key cryptography , specifically in the RSA cryptosystem , typically in the following way: [ 10 ] if y = x e ( mod n ) , {\displaystyle y=x^{e}{\pmod ...
The rules are algorithms and techniques for a variety of problems, such as systems of linear equations, quadratic equations, arithmetic progressions and arithmetico-geometric series, computing square roots approximately, dealing with negative numbers (profit and loss), measurement such as of the fineness of gold, etc. [8]
The question is whether one can usually (that is, with probability close to 1) transfer the weights between the left and right arms to balance the scale. (In case the sum of all the weights is an odd number of grams, a discrepancy of one gram is allowed.)
In mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation.
Cantor believed the continuum hypothesis to be true and for many years tried in vain to prove it. [3] It became the first on David Hilbert's list of important open questions that was presented at the International Congress of Mathematicians in the year 1900 in Paris.
The sequence produced by other choices of c can be written as a simple function of the sequence when c=1. [1]: 11 Specifically, if Y is the prototypical sequence defined by Y 0 = 0 and Y n+1 = aY n + 1 mod m, then a general sequence X n+1 = aX n + c mod m can be written as an affine function of Y: