Posts Tagged with "Euler’s totient function"

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The MathBlog tools collection updated

Monday, May 21, 2012

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Just wanted to make a bit of advertisement for the tool section of the website which have been updated and new tools added. Bjarki has been busy and developed several new tools which might come in handy for you when trying to see if a hypothesis could lead to a solution for the problem you are sitting […]

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Project Euler 71: Listing reduced proper fractions in ascending order of size.

Project Euler 72: How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000

Saturday, November 26, 2011

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I don't think it is a coincidence that this exact problem comes right now as we shall see in the solution of the problem. Problem 72 of Project Euler reads How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000?The first thing to note is that in here HCF is the same as the greatest common divisor or GCD as I usually use. The second thing to note is that we are probably looking for a very large number, but let us take a look at the problem

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Project Euler 69: Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum.

Project Euler 70: Investigate values of n for which φ(n) is a permutation of n.

Saturday, November 12, 2011

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For this problem I have taken a bit of a lazy approach with the coding and not emptied the search space, but just searched where we are most likely to find a solution. However, there are several tricks we can use when we try to find a solution. However, before babbling on, here is the problem we want to solve Find the value of n, 1 < n < 107, for which φ(n) is a permutation of n and the ratio n/φ(n) produces a minimum.Looks familiar? Well, the phi function is the same function as we looked at previously.

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Project Euler 69: Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum.

Project Euler 69: Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum.

Saturday, November 5, 2011

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We are changing topics again to a more classical number theory problem with Problem 69 of Project Euler. The problem is about factoring and readsEuler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of numbers less than n which are relatively prime to n. Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum.My first thought was to reuse some of the old problems which dealt with factoring. Problem 12 was a pretty good candidate for this. However before I got that far I realised two things.

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