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Network Name:DALnet
Channel Name:#math
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Last updated:2017-11-24 21:21:12
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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!

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Topic history
2017-09-17 - 2017-11-24
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<j [(x_i - x_j)^2]
2017-02-12 - 2017-02-18
Let a, b, c, d be pairwise distinct integers such that f(x) = (x-a)(x-b)(x-c)(x-d) - 4 has an integer root k. Show that 4k = a + b + c + d
2017-02-12 (21:08:52 - 22:08:54)
Let a, b, c, d be pairwise disctinct integers such that f(x) = (x-a)(x-b)(x-c)(x-d) - 4 has an integer root k. Show that 4k = a + b + c + d
2017-01-31 - 2017-02-12
Find all integers n such that (n^2 - 81) is a multiple of 100
2016-11-21 - 2017-01-31
2016-11-27 - 2016-12-01
Happy Birthday Jcay! may you have an exceptional year with much happiness, health and wealth.
Solve: http://mathb.in/107431
2016-11-15 - 2016-11-21
For all natural numbers n, show that 2^(n+1) divides ceil[ (1+sqrt(3))^2n ]
2016-11-14 - 2016-11-15
Beauty is not always meant to reveal itself. For it knows how to continuously drive the seekers by keeping them hungry (Elizabeth Bennet)
2016-10-30 - 2016-11-14
For x a real number, how many solutions are there in http://quiz.sueddeutsche.de/upload/9964/7694/21-03-2016_17-22-21.png ?
2016-09-13 - 2016-10-30
Given are 100 positive integers whose sum equals their product. Determine the minimum number of 1s that may occur among the 100 numbers.
2016-09-10 - 2016-09-13
In how many ways can we paint $16$ seats in a row, each red or green, in such a way that the number of consecutive seats painted in the same colour is always odd?
2016-08-15 - 2016-09-10
There are 100 ladies in a club.Each lady has had tea (in private) with exactly 56 of her friends.The Board,consisting of the 50 most old ladies,have all had tea with one another.Prove that the entire club may be split into two groups in such a way that,in each group,any lady had tea with any other.
2016-02-07 - 2016-08-15
Let a_1,a_2,a_3,... and b_1,b_2,b_3,... be two sequences of natural numbers. Prove that there are indices i<j such that a_i <= a_j and b_i <= b_j
2016-01-23 - 2016-02-07
The numbers 1,2, ... ,n^2 are placed randomly in an n × n table. Prove that there are two adjacent cells (in a row or a column) such that the numbers in them differ by at least n.
2015-12-05 - 2016-01-31
Suppose you are given n blocks, each of which weights an integral number of pounds, but less than n pounds. Suppose that the total weight of the n blocks is less than 2n. Prove that we can divide the blocks into two groups, one of which weights exactly n pounds.
2015-11-03 - 2015-12-05
Prove that there is no solution to x(x+1)(x+2)(x+3) = y^2 where x,y are natural numbers.
2015-10-30 - 2015-11-03
Prove that any coloring of the natural numbers with a finite number of colors contains integers x,y,z of the same color such that x+y=z
Bonus question: prove the same when z=x*y
get an OP question: Prove that the coloring contains integers x,y,z,w of the same color such that x+y=z and x*y=w.
2015-08-18 - 2015-10-30
We have 2^m sheets of paper, with the number 1 written on each sheet. In every step we choose two distinct sheets; if the numbers on the two sheets are a and b, then we erase these numbers and write the number a + b on both sheets. Prove that after m2^(m-1) steps the sum of the numbers on all sheets >= 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/kkP2x89d
Let 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)