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... after Wiles's proof [8] of FLT. There are congruences of various types for the Bernoulli numbers. Recent results on congruences for Bernoulli numbers of higher order can be found in [2]. We shall prove the following analog of formula (1). Theorem 1: Let ^ be a primitive Dirichlet character with modu ...
... after Wiles's proof [8] of FLT. There are congruences of various types for the Bernoulli numbers. Recent results on congruences for Bernoulli numbers of higher order can be found in [2]. We shall prove the following analog of formula (1). Theorem 1: Let ^ be a primitive Dirichlet character with modu ...
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... of N are immaterial to the mathematics—the Fibonacci numbers are here no matter what. As for the gambler's fortune, that is another story. The expected value of the game is easily shown to have the form ...
... of N are immaterial to the mathematics—the Fibonacci numbers are here no matter what. As for the gambler's fortune, that is another story. The expected value of the game is easily shown to have the form ...
Lecture Notes for Section 8.2
... Big Idea: There are rules for how to multiply and divide expressions with radicals which can lead to simpler radical expressions. Big Skill: You should be able to simplify radicals by switching them between products or quotients of radicals and radicals of products or quotients. Product Rule for Squ ...
... Big Idea: There are rules for how to multiply and divide expressions with radicals which can lead to simpler radical expressions. Big Skill: You should be able to simplify radicals by switching them between products or quotients of radicals and radicals of products or quotients. Product Rule for Squ ...
Final stage of Israeli students competition, 2010. Duration: 4.5 hours
... 1. Prove that there exists an integer n, such that n2 + 3 is divisible by 75770. Solution. There’s nothing so special about this year, so we shall prove that for every natural m, we can find n such that n2 + 3 is divisible by 7m. The base of induction is simple: 22 + 3 is divisible by 7. The step of ...
... 1. Prove that there exists an integer n, such that n2 + 3 is divisible by 75770. Solution. There’s nothing so special about this year, so we shall prove that for every natural m, we can find n such that n2 + 3 is divisible by 7m. The base of induction is simple: 22 + 3 is divisible by 7. The step of ...
Lecture on Polynomial Functions
... numbers include numbers like 1, –2, 15, ½, 2/3, and –51/3. Irrational Numbers – irrational numbers are numbers that are not rational, i.e., with the above definition, irrational numbers do not terminate or repeat in their decimal form. Irrational numbers include numbers like ...
... numbers include numbers like 1, –2, 15, ½, 2/3, and –51/3. Irrational Numbers – irrational numbers are numbers that are not rational, i.e., with the above definition, irrational numbers do not terminate or repeat in their decimal form. Irrational numbers include numbers like ...
Elementary mathematics
Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels. The most basic topics in elementary mathematics are arithmetic and geometry. Beginning in the last decades of the 20th century, there has been an increased emphasis on problem solving. Elementary mathematics is used in everyday life in such activities as making change, cooking, buying and selling stock, and gambling. It is also an essential first step on the path to understanding science.In secondary school, the main topics in elementary mathematics are algebra and trigonometry. Calculus, even though it is often taught to advanced secondary school students, is usually considered college level mathematics.