System.ArithmeticException

In the source of that BigInteger, there is:

// maximum length of the BigInteger in uint (4 bytes)
// change this to suit the required level of precision.
private const int maxLength = 70;

The length is counted in limbs, each limb is 32 bits in this implementation. Additionally, the topmost bit of the topmost limb is treated as a sign bit. Therefore, without changing the source the maximum number that can be stored in this kind of BigInteger (this limit does not apply to the BigInteger in System.Numerics) is 2^70*32-1-1, or in other words, there are 2239 "normal" bits available.

That allows for some fairly big integers, but not big enough: according to Wolfram Alpha fib(3227) requires just over 2239 bits, therefore it does not fit.

Following the link from @Mishhl the fix is

public class FloatingPointReset
{
    [DllImport("msvcr110.dll", CallingConvention = CallingConvention.Cdecl)]
    public static extern int _fpreset();


    public static void Action()
    {
        // Reset the Floating Point (When called from External Application there was an Overflow exception)
        _fpreset();
    }
}

It's caused by something in an included DLL resetting the FP into a state that isn't compatible with WPF/C#/Microsoft DLL's. Delphi/CPPB does this by default.

So in either the window constructor or App() constructor just do

FloatingPointReset.Action();

You may need to change the following to reference any version of msvcr###.dll

[DllImport("msvcr110.dll", CallingConvention = CallingConvention.Cdecl)]

e.g.

[DllImport("msvcr70.dll", CallingConvention = CallingConvention.Cdecl)]

My guess is that you're running out of memory in the byte[] array.

You can try breaking the file down and reading it in chunks.

I found a code example from a Google search to get you started:

C# file downloader AKA Response.BinaryWrite

using System;
using System.IO;
using System.Web;

public class Download
{
    public static void SmallFile(string filename, string filepath, string contentType)
    {
        try
        {
            FileStream MyFileStream = new FileStream(filepath, FileMode.Open, FileAccess.Read, FileShare.Read);
            long FileSize;
            FileSize = MyFileStream.Length;
            byte[] Buffer = new byte[(int)FileSize];
            MyFileStream.Read(Buffer, 0, (int)MyFileStream.Length);
            MyFileStream.Close();
            HttpContext.Current.Response.ContentType = contentType;
            HttpContext.Current.Response.AddHeader("Content-Disposition", "attachment;filename=" + HttpUtility.UrlEncode(filename, System.Text.Encoding.UTF8));
            HttpContext.Current.Response.BinaryWrite(Buffer);             
        }
        catch
        {
            HttpContext.Current.Response.ContentType = "text/html";
            HttpContext.Current.Response.Write("Downloading Error!");
        }
        HttpContext.Current.Response.End();
    }

    public static void LargeFile(string filename, string filepath, string contentType)
    {
        Stream iStream = null;
        // Buffer to read 10K bytes in chunk
        //byte[] buffer = new Byte[10000];
        // Buffer to read 1024K bytes in chunk
        byte[] buffer = new Byte[1048576];

        // Length of the file:
        int length;
        // Total bytes to read:
        long dataToRead;

        try
        {
            // Open the file. 
            iStream = new FileStream(filepath, FileMode.Open, FileAccess.Read, FileShare.Read);

            // Total bytes to read:
            dataToRead = iStream.Length;
            HttpContext.Current.Response.ContentType = contentType;
            HttpContext.Current.Response.AddHeader("Content-Disposition", "attachment; filename=" + HttpUtility.UrlEncode(filename, System.Text.Encoding.UTF8));

            // Read the bytes.
            while (dataToRead > 0)
            {
                // Verify that the client is connected.
                if (HttpContext.Current.Response.IsClientConnected)
                {
                    // Read the data in buffer.
                    length = iStream.Read(buffer, 0, 10000);

                    // Write the data to the current output stream.
                    HttpContext.Current.Response.OutputStream.Write(buffer, 0, length);

                    // Flush the data to the HTML output.
                    HttpContext.Current.Response.Flush();

                    buffer = new Byte[10000];
                    dataToRead = dataToRead - length;
                }
                else
                {
                    //prevent infinite loop if user disconnects
                    dataToRead = -1;
                }
            }
        }
        catch (Exception ex)
        {
            // Trap the error, if any.
            //HttpContext.Current.Response.Write("Error : " + ex.Message);
            HttpContext.Current.Response.ContentType = "text/html";
            HttpContext.Current.Response.Write("Error : file not found");                 
        }
        finally
        {
            if (iStream != null)
            {
                //Close the file.
                iStream.Close();
            }
            HttpContext.Current.Response.End();
            HttpContext.Current.Response.Close();             
        }         
    }

    public static void ResumableFile(string filename, string fullpath, string contentType)
    {
        try
        {
            FileStream myFile = new FileStream(fullpath, FileMode.Open, FileAccess.Read, FileShare.ReadWrite);
            BinaryReader br = new BinaryReader(myFile);
            try
            {
                HttpContext.Current.Response.AddHeader("Accept-Ranges", "bytes");
                HttpContext.Current.Response.Buffer = false;
                long fileLength = myFile.Length;
                long startBytes = 0;

                //int pack = 10240; //10K bytes
                int pack = 1048576; //1024K bytes

                if (HttpContext.Current.Request.Headers["Range"] != null)
                {
                    HttpContext.Current.Response.StatusCode = 206;
                    string[] range = HttpContext.Current.Request.Headers["Range"].Split(new char[] { '=', '-' });
                    startBytes = Convert.ToInt64(range[1]);
                }
                HttpContext.Current.Response.AddHeader("Content-Length", (fileLength - startBytes).ToString());
                if (startBytes != 0)
                {
                    HttpContext.Current.Response.AddHeader("Content-Range", string.Format(" bytes {0}-{1}/{2}", startBytes, fileLength - 1, fileLength));
                }
                HttpContext.Current.Response.AddHeader("Connection", "Keep-Alive");
                HttpContext.Current.Response.ContentType = contentType;
                HttpContext.Current.Response.AddHeader("Content-Disposition", "attachment;filename=" + HttpUtility.UrlEncode(filename, System.Text.Encoding.UTF8));

                br.BaseStream.Seek(startBytes, SeekOrigin.Begin);
                int maxCount = (int)Math.Floor((double)((fileLength - startBytes) / pack)) + 1;

                for (int i = 0; i < maxCount; i++)
                {
                    if (HttpContext.Current.Response.IsClientConnected)
                    {
                        HttpContext.Current.Response.BinaryWrite(br.ReadBytes(pack));
                    }
                    else
                    {
                        i = maxCount;
                    }
                }
            }
            catch
            {
                HttpContext.Current.Response.ContentType = "text/html";
                HttpContext.Current.Response.Write("Error : file not found");
            }
            finally
            {
                br.Close();
                myFile.Close();
            }
        }
        catch
        {
            HttpContext.Current.Response.ContentType = "text/html";
            HttpContext.Current.Response.Write("Error : file not found");
        }
    }     
}

I am not sure of the root cause yet but the solution is here :
http://social.msdn.microsoft.com/forums/en-US/wpf/thread/a31f9c7a-0e15-4a09-a544-bec07f0f152c

Seems to be a popular bug :)