The Frobenius Problem and Its Generalizations
... To get a representation for larger numbers, we use the extended Euclidean algorithm to find integers e, f such that ex − fy = 1. We just add the appropriate multiple of this equation, reducing, if necessary, by (−y )x + xy or yx + (−x)y if a coefficient becomes negative. For example, for (x, y ) = [ ...
... To get a representation for larger numbers, we use the extended Euclidean algorithm to find integers e, f such that ex − fy = 1. We just add the appropriate multiple of this equation, reducing, if necessary, by (−y )x + xy or yx + (−x)y if a coefficient becomes negative. For example, for (x, y ) = [ ...
Powers of rationals modulo 1 and rational base number systems
... and allows us to make some progress on the commonly studied generalization of Mahler’s problem — as we explain at the end of this introduction. The idea of non-standard representation systems of numbers is far from being original and there have been extensive studies of these, from a theoretical st ...
... and allows us to make some progress on the commonly studied generalization of Mahler’s problem — as we explain at the end of this introduction. The idea of non-standard representation systems of numbers is far from being original and there have been extensive studies of these, from a theoretical st ...
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... alternate in sign, then -3 is a lower bound. Remember that the number zero can be considered positive or negative. ...
... alternate in sign, then -3 is a lower bound. Remember that the number zero can be considered positive or negative. ...
INTERNATIONAL INDIAN SCHOOL, RIYADH CLASS: X SUBJECT
... 47) A sum of Rs 1400 is to be used to give 7 cash prizes to students of a school for their overall academic Performance if each prize is Rs40 less than the preceding price, find the value of each of the prizes. ...
... 47) A sum of Rs 1400 is to be used to give 7 cash prizes to students of a school for their overall academic Performance if each prize is Rs40 less than the preceding price, find the value of each of the prizes. ...
Use the five properties of exponents to simplify each
... a company can sell per month and the price of each calculator p is given by x = 1700 - 100p. Find the price at which a calculator should be sold to produce a monthly revenue of $7000. (Hint: Revenue = xp.) ...
... a company can sell per month and the price of each calculator p is given by x = 1700 - 100p. Find the price at which a calculator should be sold to produce a monthly revenue of $7000. (Hint: Revenue = xp.) ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.