Posts Tagged with "Continued fractions"

tools

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 66: Investigate the Diophantine equation x^2 − Dy^2 = 1.

Project Euler 66: Investigate the Diophantine equation x^2 − Dy^2 = 1.

Saturday, October 22, 2011

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Based on the problem description for Problem 66 of Project Euler I thought we had left the continued fractions for a while. Once I started reading up on the maths behind it and trying to solve the problem I got quite a lot wiser. But let's start from the beginning and look at the problem description which readsConsider quadratic Diophantine equations of the form: x2 – Dy2 = 1 Find the value of D 1000 in minimal solutions of x for which the largest value of x is obtained.

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Project Euler 65: Find the sum of digits in the numerator of the 100th convergent of the continued fraction for e.

Project Euler 65: Find the sum of digits in the numerator of the 100th convergent of the continued fraction for e.

Saturday, October 15, 2011

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They really went crazy with the whole continued fractions theme. Project Euler's problem 65 as this one is about the continued fraction of e. The problem readsFind the sum of digits in the numerator of the 100th convergent of the continued fraction for e.We are only interested in the numerator, and if we investigate that we will rather quickly find a patter which is consistent with given continued fraction for e.

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Project Euler 64:How many continued fractions for N ≤ 10000 have an odd period?

Project Euler 64:How many continued fractions for N ≤ 10000 have an odd period?

Saturday, October 8, 2011

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Problem 57 was all about continued fractions, and in Problem 64 of Project Euler we are visiting that subject again. The problem readsHow many continued fractions for N ≤ 10000 have an odd period?I shall be the first person here to admit that all I got from the problem description was the question, the helping text didn’t help me at all. So I had to ask uncle wiki how to solve this problem, and it returned me an algorithm which I could use.

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