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The largest minimal x has 39 digits.Perlkonig wrote:Can somebody confirm this, please? I was so sure my code was correct, but the max value it's finding is 30 digits long, and the value for D is not being accepted. Thanks!daniel.is.fischer wrote:Yes, the value exceeds 64-bit range, it's a 38-digit number.
I agree with daniel.is.fisher : 38 digits : 16421... <end snipped>thundre wrote:The largest minimal x has 39 digits.Perlkonig wrote:Can somebody confirm this, please? I was so sure my code was correct, but the max value it's finding is 30 digits long, and the value for D is not being accepted. Thanks!daniel.is.fischer wrote:Yes, the value exceeds 64-bit range, it's a 38-digit number.
That's what I get for y.Francky wrote:I agree with daniel.is.fisher : 38 digits : (snip)thundre wrote:The largest minimal x has 39 digits.
You shouldn't need more than four digits.Find the value of D ≤ 1000 in minimal solutions of x for which the largest value of x is obtained.
brandish wrote:Don't know where else to write this, but the answer box only accepts 30 digits at the moment. Can this be changed so my hopefully correct answer can get accepted?
4 digits should be enough to represent a number not exceeding 1000.... Find the value of D ≤ 1000" ...
It is implied from the statement about square D and the examples that we are looking for x and y positive integers.Montago wrote:... So ... Why is x=1 and y=0 not a solution for ALL D>0 ??
Please don't post results in this forum, and use the existing topic if one already exists.vivekchaudhary wrote:I'm getting different results using Pell’s Equation and brute force!
Pell's equation results in <snip>, but for <snip>, so <snip> should be the answer.
Can someone please cross-verify my results?
Problem 66 [https://projecteuler.net/problem=66]
EDIT by moderator: merged topic and removed spoilers.
hk, I read your post on Diophantine Equations. The problem 66 is a special case, i.e. Pell's equation.hk wrote: Wed Jul 13, 2011 3:25 pm Well, if you look up http://en.wikipedia.org/wiki/Diophantine_equation and look at "Examples of Diophantine Equations" it's there, isn't it? (third example).
What it boils down to is that people are supposed to do this bit of research by themselves and find out what it is about.
The meta goal is to get proficient in this kind of web based self learning, based on the information given to you by the problem statement. That's why I still think that people should abstain from giving such extra information in this forum.
For me you don't need to remove your information as this discussion in itself is very instructive imho, telling people what they are supposed to do.
convergents to the regular continued fraction
Well that link is already a good start. Some of the links onwards from that page should also help. As a general point, I always find the Wolfram MathWorld pages very useful too. For the Pell Equation in particular, there are plenty of resources around the web, at various levels. It's worth spending a bit of time getting to grips with the Pell Equation and Continued Fractions, as they are often very useful in these types of problems.Alex-82w4 wrote: Mon Feb 06, 2017 2:26 pm
hk, I read your post on Diophantine Equations. The problem 66 is a special case, i.e. Pell's equation.
