Senior Math Circles Sequences and Series I 1 Polygonal
... Question 1.3. What is the formula for the n-th pentagonal number? Solution. Let un denote the n-th pentagonal number. We assume that un is a quadratic in n. This assumption is reasonable, since the size of a 2-dimensional object in general grows quadratically in n. Write un = an2 + bn + c. Then u1 ...
... Question 1.3. What is the formula for the n-th pentagonal number? Solution. Let un denote the n-th pentagonal number. We assume that un is a quadratic in n. This assumption is reasonable, since the size of a 2-dimensional object in general grows quadratically in n. Write un = an2 + bn + c. Then u1 ...
Problems - NIU Math
... This section begins the study of fields in earnest. Besides the standard examples Q, R, and C from high school algebra, you should become familiar with Zp (viewed as a field) and with the other examples in the text. The axioms of field are the ones we need to work with polynomials and matrices, so t ...
... This section begins the study of fields in earnest. Besides the standard examples Q, R, and C from high school algebra, you should become familiar with Zp (viewed as a field) and with the other examples in the text. The axioms of field are the ones we need to work with polynomials and matrices, so t ...
word
... 7. Consider the following sketch of an algorithm called ProcessArray which performs some unspecified operation on a subarray A[ p r ] . ...
... 7. Consider the following sketch of an algorithm called ProcessArray which performs some unspecified operation on a subarray A[ p r ] . ...
Full text
... Let p be a prime number and let Zp and Qp denote the ring of p-adic integers and the field ofp-adic numbers, respectively. For any uniformly differentiable function / : Zp —> Qp, we define the Volkenborn integral of/by ...
... Let p be a prime number and let Zp and Qp denote the ring of p-adic integers and the field ofp-adic numbers, respectively. For any uniformly differentiable function / : Zp —> Qp, we define the Volkenborn integral of/by ...
Chinese remainder theorem
The Chinese remainder theorem is a result about congruences in number theory and its generalizations in abstract algebra. It was first published in the 3rd to 5th centuries by the Chinese mathematician Sun Tzu.In its basic form, the Chinese remainder theorem will determine a number n that, when divided by some given divisors, leaves given remainders. For example, what is the lowest number n that when divided by 3 leaves a remainder of 2, when divided by 5 leaves a remainder of 3, and when divided by 7 leaves a remainder of 2?