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 Network Name: DALnet Channel Name: #math Last users: 18 Last updated: 2019-11-20 20:09:30 Current topic: Find all pairs (k, n) of positive integers such that k! = (2^n − 1)(2^n − 2)(2^n − 4)*...*(2^n − 2^(n−1))

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Day | Week | Month | Year    Topic history
 2019-09-25 - 2019-11-20 Find all pairs (k, n) of positive integers such that k! = (2^n − 1)(2^n − 2)(2^n − 4)*...*(2^n − 2^(n−1)) 2019-05-29 - 2019-09-25 http://mathworld.wolfram.com/Let p be an odd prime. How many non-empty subsets of {1,2,...,p-2,p-1} have a sum which is divisible by p 2019-05-25 - 2019-05-29 Let p be an odd prime. How many non-empty subsets of {1,2,...,p-2,p-1} have a sum which is divisible by p 2019-03-04 - 2019-05-25 http://mathworld.wolfram.com/https://pastebin.com/M2zDkUD3We have to make 24 by using 1, 3, 4, and 6. We can use +,-,*,/. and each number exactly once 2018-06-18 - 2019-03-04 https://pastebin.com/M2zDkUD3We have to make 24 by using 1, 3, 4, and 6. We can use +,-,*,/. and each number exactly once 2018-06-10 - 2018-06-18 We have to make 24 by using 1, 3, 4, and 6. We can use +,-,*,/. and each number exactly once 2018-02-23 - 2018-06-10 Let S be a bounded, closed set on the real plane such that the distance between any two points < 1. Show that S lies within a circle of radius 1/sqrt(3) 2017-09-17 - 2018-02-23 For each rational number p/q in (0,1) set an open interval of size 1/(2q^2) centered on p/q. Show that sqrt(2)/2 is not in any of these intervals! 2017-09-14 - 2017-09-17 For each rational number p/q in (0,1) set an open interval of size 1/(2q^2) centered on p/q. Show that sqrt(2)/2 is not in any of these intervals!Congrats Gauss!Congrats Nick!Congrats Jcay! 2017-08-24 - 2017-09-14 For n a natural number, show that ceil[sqrt(n) + sqrt(n+1)] = ceil[sqrt(4n + 2)]Congrats Gauss!Congrats Nick!Congrats Jcay! 2017-06-15 - 2017-08-24 Let a,b,c be non-negative real numbers, no two of which are equal. Prove that a^2/(b-c)^2 + b^2/(c-a)^2 + c^2/(a-b)^2 > 2.Congrats Gauss! 2017-04-22 - 2017-06-15 Let a,b,c be non-negative real numbers, no two of which are equal. Prove that a^2/(b-c)^2 + b^2/(c-a)^2 + c^2/(a-b)^2 > 2. 2017-04-13 - 2017-04-22 Prove that n! + 1 is not a square number for all integer n>7 2017-02-18 - 2017-04-13 Let x_1, ..., x_n be the n n-th roots of unity. Evaluate Prod_i= 4^m 2015-07-11 - 2015-08-18 For which integers k does (x^2 - x + k) divide (x^13 + x + 90)? 2015-07-10 - 2015-07-11 For which integers k does (x^2 - x + k) divide (x^13 + x +90)? 2015-06-10 - 2015-07-10 A rectangular table has 100 coins with unit radius, placed on it such that none of the coins overlap, and it is impossible to place any more coins on the table without causing an overlap. Using this specific configuration, find a special configuration of 400 coins which covers the table with overlaps. 2015-05-01 - 2015-06-10 http://pastebin.com/kkP2x89dLet a,b be positive integers. Show that if (4ab-1) divides ((4a^2) - 1)^2 then a=b. 2015-04-25 - 2015-04-30 A number written in base 10 is a string of 3^2013 digit 3s. No other digit appears. Find the highest power of 3 which divides this number.http://pastebin.com/kkP2x89d 2015-04-22 - 2015-04-25 A number written in base 10 is a string of 3^2013 digit 3s. No other digit appears. Find the highest power of 3 which divides this number. 2015-03-27 - 2015-04-22 Let n be a natural number. Prove that [floor(n/1) + floor(n/2) + floor(n/3) + .... + floor(n/n)] + floor(sqrt(n)) is always even 2015-03-12 - 2015-03-27 For each n show that there is a Fibonacci number that ends in at least n zeros.Rest in peace Terry Pratchett, we loved you and your books. 2015-03-02 - 2015-03-12 For each n show that there is a Fibonacci number that ends in at least n zeros. 2015-02-28 - 2015-03-01 In a country there are several cities and several roads. Every road connects to exactly 2 cities. Out of every city there exist at least 3 roads. Prove that there is a cycle, the number of cities in which is not divisible by 3. 2015-02-21 - 2015-02-28 Suppose you are given n blocks, each of which weighs an integral number of pounds, but less than n pounds. Suppose also that the total weight of the n blocks is less than 2n pounds. Prove that the blocks can be divided into two groups, one of which weighs exatly n pounds. 2015-02-21 (15:02:34 - 17:02:35) Suppose you are given n blocks, eah of which weighs an integral number of pounds, but less than n pounds. Suppose also that the total weight of the n blocks is less than 2n pounds. Prove that the blocks can be divided into two groups, one of which weighs exatly n pounds. 2015-02-20 - 2015-02-21 Suppose you are given n blocks, eah of which weigts an integral number of pounds, but less than n pounds. Suppose also that the total weight of the n bloks is less than 2n pounds. Prove that the blocks can be divided into two groups, one of which weighs exatly n pounds. 2015-02-13 - 2015-02-20 Let n be a fixed positive integer. Find the sum of all positive integers with the following property: In base 2, it has exactly 2n digits consisting of n 1’s and n 0’s. The first digit cannot be 0. 2015-02-09 - 2015-02-13 Suppose that a_0=1 and a_(n+1) = a_n + e^(-a_n) for n=0,1,2,... Does a_n - ln(n) have a finite limit as n tends to infinity? 2015-02-05 - 2015-02-09 Each vertex of a finite graph can be colored either black or white. Initially all vertices are black. We are allowed to pick a vertex P and change the color of P and all of its neighbours. Is it possible to change the colour of every vertex from black to white by a sequence of operations of this type? 2015-01-26 - 2015-02-05 Let m, n be natural numbers. Show that 4mn − m − n can never be a square.Show that for all n >= 6 there exists natural numbers (a_1,...,a_n) such that 1/a_1^2 + ... + 1/a_n^2 = 1. 2015-01-03 - 2015-01-26 Let m, n be natural numbers. Show that 4mn − m − n can never be a square. 2014-12-22 - 2015-01-03 Given an integer n>=2 prove that the product of all primes lower or equal than n is lower or equal than 4^(n-1)