Project Euler Forum

I found out that problem can be solved by finding first 15 integer terms of sequence sqrt(*snip*). I've tried to get then in many different ways, using c++ or mathematica, and always my algorithms are too slow. I could use some hint to find those, or some another idea to solve this problem.

Killa

Can you perhaps spot a pattern among the first few values of n for which sqrt(*snip*) is integer?

Have fun solving!

To be honest i've seen this integers first time in my life (and im not new to math; )).

Friend helped me to solve it, so problem is already gone: ).

If you're not new to math you've probably heard of Pell's equation.
In this case you're asked to find solutions to a Pell-like quadratic diophantine equation
So here are two keywords you can use to solve this kind of problem.
This kind of questions are not uncommon here.

Yeah, i've been thinking some about problem 140, kinda similiar to 137 and i found the connection with pell equasions, in some days i'll certainly find the answers and learn some new things.

Thanks for the hints: )

Can someone who solved the problem send me a PM explaining hyperdex's solution. In particular, I don't understand why he does this:

hyperdex wrote:if the numerator is (~) mod (~), we check to see if it leads to a solution. If the numerator is (~) mod (~), we check to see if (~) the numerator leads to a solution. (Since we are looking for (~), we don't need to check any further multiples of the numerator.)

Why don't we need to check further multiples? His post is the twelfth on the first page. Thank you.

PM sent.

I think there is some mistake on the wording of this question.

The question does say that we are considering only values of x such that Af(x) is a positive integer.

However, there are solutions for negative values of x.

IE x = -2 and x = 1/2 both result in Af(x) = 2


However for the sake of the problem, I guess that Af(x) = 2 is rational for both values of X, positive and negative

I solved this problem...

An amazing problem, props to you guys

RishadanPort wrote: Mon Aug 05, 2019 11:22 pm IE x = -2 and x = 1/2 both result in Af(x) = 2

$A_F(-2) \neq 2$. It doesn't converge.

Oh!

Sorry then. thanks for the reply.

This is to confirm (I am pretty sure this is true) that the first nugget is the 1/2 explained in the problem statement. I have now found (bug in code) that was leading me to question whether this one wasn’t counted in the tally, but it is indeed nugget #1. Maybe that will help another lost soul…

Now off to find 11 thru 15…