Re: Question on modular algebra

On 16 mar, 10:54, "Dani Camps" <danicamp...@xxxxxxxxx> wrote:
On 15 mar, 16:46, Peter Pearson <ppear...@xxxxxxxxxxxxxxx> wrote:

On 14 Mar 2007 08:43:26 -0700, Dani Camps <danicamp...@xxxxxxxxx> wrote:

I have a sequence generated with the following expression

A(x)=(d + a*x) (mod n)

Where 0<=d<n, and a and n are coprimes, i.e gcd(a,n)=1.
Consider r consecutive values of the sequence A(x)
starting from 0, so {A(0) ... A(r-1)} where 0<=r<n. What I
want to know is how many values of the subset {A(0)
... A(r-1)} are above my threshold j.

An approximate solution would be simple. Do you need an
exact solution? Faster than just counting them?

To email me, substitute nowhere->spamcop, invalid->net.


What I am looking for is the exact value in a close formula. I need
this in order to proof something, so I am not interested in an
algorithm. Do you have any idea ? An approximation, or better a bound,
can be a starting point.

Best Regards


Actually what I need to proof is that r/(m-1) is bigger than sth, so I
need a lower bound for r/(m-1). Where r is the lentgh of the sequence,
and m is the number of elements in the sequence {A(0) ... A(r-1)}
above/below the threshold j.