Pretty Primes
... Every natural number is constructed out of its own set of primes with indices, “glued together” by multiplication. This rule is so powerful, that most of the problems where you have to find some natural numbers satisfying some special conditions are solved based on products and their close relatives ...
... Every natural number is constructed out of its own set of primes with indices, “glued together” by multiplication. This rule is so powerful, that most of the problems where you have to find some natural numbers satisfying some special conditions are solved based on products and their close relatives ...
More properties in Goldbach`s Conjecture
... The strong formulation of Goldbach conjecture, which is the subject of this paper, is much more difficult than the above weak one. Using the above method of Vinogradov [8], in separate works Chudakov [17], van der Corput [18] and Estermann [19] showed that almost all even number can be written as a ...
... The strong formulation of Goldbach conjecture, which is the subject of this paper, is much more difficult than the above weak one. Using the above method of Vinogradov [8], in separate works Chudakov [17], van der Corput [18] and Estermann [19] showed that almost all even number can be written as a ...
Full text
... A polynomial p(x) divides another polynomial q(x) if q(x0) = 0 for all xQ such that p(x 0 ) = 0. Letting p(x) = 1 + x + x2 + x3 + xh , we see that p(ar) is the cyclotomic polynomial (x5 - I) / (x - 1 ) 9 which has four complex zeros equal to the complex fifth roots of unity. Let 0 denote any of thes ...
... A polynomial p(x) divides another polynomial q(x) if q(x0) = 0 for all xQ such that p(x 0 ) = 0. Letting p(x) = 1 + x + x2 + x3 + xh , we see that p(ar) is the cyclotomic polynomial (x5 - I) / (x - 1 ) 9 which has four complex zeros equal to the complex fifth roots of unity. Let 0 denote any of thes ...
Chapter 5 Operations with Algebraic Expressions
... much as a soft drink. If a soft drink costs s cents, express the total cost of a cheeseburger, an order of fries, and a soft drink in terms of s. 34. Jack deposited some money in his savings account in September. In October he deposited twice as much as in September, and in November he deposited one ...
... much as a soft drink. If a soft drink costs s cents, express the total cost of a cheeseburger, an order of fries, and a soft drink in terms of s. 34. Jack deposited some money in his savings account in September. In October he deposited twice as much as in September, and in November he deposited one ...
MATHEMATICS INDUCTION AND BINOM THEOREM
... discussion is about positive integers sets Three steps to prove (using mathematics induction) that “P(n) is true for all n positive integers”: 1. Basic step: prove that P(1) is true 2. Inductive step: Assumed that P(k) is true, it can be shown that P(k+1) is true for all k 3. Conclusion: n P(n) i ...
... discussion is about positive integers sets Three steps to prove (using mathematics induction) that “P(n) is true for all n positive integers”: 1. Basic step: prove that P(1) is true 2. Inductive step: Assumed that P(k) is true, it can be shown that P(k+1) is true for all k 3. Conclusion: n P(n) i ...
INTERNATIONAL INDIAN SCHOOL, RIYADH SUBJECT
... 12. The sum of digits of a two digit numbers is 7. If the digits are reversed, the new number decreased by 2 equals twice the original Number.Find the number ...
... 12. The sum of digits of a two digit numbers is 7. If the digits are reversed, the new number decreased by 2 equals twice the original Number.Find the number ...
Integers and Division
... • Branch of mathematics that includes (among other things): – divisibility – greatest common divisor – modular arithmetic ...
... • Branch of mathematics that includes (among other things): – divisibility – greatest common divisor – modular arithmetic ...
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.