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Binomial number
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131	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
132	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
133	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
134	Partitions in the quintillions or Billions of congruences Fredrik Johansson November 2011 Add to Reading List Source URL: fredrikj.net Language: English - Date: 2013-04-03 06:22:12 Combinatorics Factorial Bernoulli number Binomial coefficient Exponentiation Pi Partition Prime number Logarithm Mathematics Integer sequences Number theory
135	2011 U OF I FRESHMAN MATH CONTEST Solutions 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 digi Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2011-10-01 17:22:28 Combinatorics Number theory Mathematical series Complex analysis Binomial coefficient Factorial Pi Summation Proof that π is irrational Mathematics Mathematical analysis Integer sequences
136	On the log-concavity of the degenerate Bernoulli 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: 2011-10-07 14:23:41 Spectral theory Number theory Operator theory Bernoulli number Topology Binomial coefficient Λ-ring Sturm–Liouville theory Mathematics Mathematical analysis Integer sequences
137	UIUC UNDERGRADUATE MATH CONTEST April 8, [removed]Determine, without numerical calculations, which of the two numbers √ Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2006-04-08 17:58:20 Ring theory Elementary mathematics Combinatorics Elementary number theory Integer Liouville number Binomial coefficient Mathematics Abstract algebra Algebraic number theory
138	2014 UI UNDERGRADUATE MATH CONTEST Solutions 1. (a) Does there exist a multiple of 2013 whose decimal representation ends in the digits 2014? Explain! (b) Does there exist a power of 2 whose decimal representation ends i Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2014-02-15 21:13:47 Integer sequences Number theory Exponentials Binomial coefficient Factorial Summation Exponential function Proof that π is irrational Basel problem Mathematics Mathematical analysis Combinatorics
139	UIUC UNDERGRADUATE MATH CONTEST April 12, 2003 Solutions 1. Let Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2003-04-12 16:50:35 Integer sequences Number theory Factorial Proof that π is irrational Binomial coefficient Mathematics Mathematical analysis Combinatorics
140	U OF I UNDERGRADUATE MATH CONTEST MARCH 7, 2009 Solutions − denote the integer obtained by reversing the 1. Given a nonnegative integer n, let ← n Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2009-03-07 17:49:43 Combinatorics Exponentials Factorial Exponentiation Binomial coefficient Proof that π is irrational Mathematics Integer sequences Number theory

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