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Binomial coefficient
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231	Graphs and Combinatorics manuscript No. (will be inserted by the editor) Colorful Strips Greg Aloupis⋆ · Jean Cardinal⋆ · S´ebastien Collette⋆ · Shinji Imahori⋆⋆ · Matias Korman⋆ · Add to Reading List Source URL: www.cs.berkeley.edu Language: English - Date: 2012-04-02 07:03:44 Probabilistic method Permutation Edge coloring Random permutation statistics Binomial coefficient Mathematics Combinatorics Graph coloring
232	Bernoulli numbers and generalized factorial sums Paul Thomas Young Department of Mathematics, College of Charleston Charleston, SC[removed]removed] Add to Reading List Source URL: youngp.people.cofc.edu Language: English - Date: 2010-06-25 15:31:33 Combinatorics Modular arithmetic Bernoulli number Topology Bernoulli polynomials Binomial coefficient P-adic number Summation Factorial Mathematics Number theory Integer sequences
233	2011 U OF I FRESHMAN MATH CONTEST 1. Let x = 0.[removed][removed]be the number whose decimal expansion consists of the sequence of natural numbers written next to each other. (a) Determine the 2011th digit after th Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2011-10-02 10:35:20 Arithmetic Least common multiple Mathematical proof Pi Pythagorean triple Binomial coefficient Mathematics Elementary arithmetic Number theory
234	UIUC Mock Putnam Exam[removed]Solutions Problem 1. Without any numerical calculations, determine which of the two numbers eπ and π e is larger. Solution. Let a = eπ and b = π e . We will show that a > b. Since Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2005-10-11 15:50:00 Integer sequences Polynomial Exponentiation Logarithm Pi Factorial Proof that π is irrational Binomial coefficient Mathematics Mathematical analysis Combinatorics
235	U OF I MOCK PUTNAM EXAM SEPT. 29, [removed]Suppose P (x) is a polynomial with integer coefficients such that none of the values P (1), . . . , P[removed]is divisible by[removed]Prove that P (n) 6= 0 for all integers n. 2. Fi Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2009-09-30 19:05:13 Algebraic number theory Integer sequences Elementary number theory Integer Ring theory Number Square-free integer Binomial coefficient Mathematics Abstract algebra Number theory
236	UIUC Mock Putnam Exam[removed]Solutions Problem 1. Let a1 = 1, a2 = 1, a3 = −1, and for n > 3 define an by an = an−1 an−3 . Find a2006 . Solution. Computing the first 10 terms of the sequence {an }, we obtain Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2006-10-08 16:27:20 Fibonacci number Summation Mathematical induction Factorial Recurrence relation Generating function Binomial coefficient Formal power series Mathematics Combinatorics Integer sequences
237	2010 U OF I MOCK PUTNAM EXAM Solutions 1. (a) Given a set with n elements (where n is a positive integer), prove that exactly 2n−1 of its subsets have an odd number of elements. (b) Determine, with proof, the number of Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2010-10-02 21:33:48 Number theory Factorial Equidistributed sequence Limit superior and limit inferior Summation Binomial coefficient Mathematics Integer sequences Combinatorics
238	2011 U OF I MOCK PUTNAM CONTEST 1. [Variation of A2, Putnam[removed]The sequence of digits[removed][removed] ... is obtained by writing out the natural numbers in order. Let f (n) denote the position of the Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2011-10-02 10:33:09 Integer sequences Calculus Binomial coefficient Factorial Series Mathematical series Binomial series Mixing Mathematics Mathematical analysis Combinatorics
239	On the binary expansion of the odd Catalan numbers Florian Luca Instituto de Matem´aticas Universidad Nacional Aut´onoma de M´exico C.P[removed], Morelia, Michoac´an, M´exico Add to Reading List Source URL: youngp.people.cofc.edu Language: English - Date: 2010-02-17 14:43:11 Combinatorics Number theory Complex analysis Pi Factorial Binomial coefficient Mathematics Mathematical analysis Integer sequences
240	Seven Staggering Sequences N. J. A. Sloane Algorithms and Optimization Department AT&T Shannon Lab Florham Park, NJ 07932–0971 Email address: [removed] Add to Reading List Source URL: neilsloane.com Language: English - Date: 2012-01-02 21:20:56 Combinatorics Recurrence relations On-Line Encyclopedia of Integer Sequences Sequence Generating function Collatz conjecture Summation Factorial Binomial coefficient Mathematics Integer sequences Number theory

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