I had the following on another computer:

Let me rephrase the problem as:
Find the value of 2^99 (mod 99).

Using Excel as my calculator, it does not go conveniently go beyond 2^32 it is necessary to split the value of 99 into smaller powers.
Considering 99 as being 3 * 32 + 3, then I have these values:
Index      2^Index         mod 99
32        4294967296        4
32        4294967296        4
32        4294967296        4
3                  8        8
(Total 99)

Now 2^32(mod 99) = 4294967296(mod 99)= 4
and 8(mod 99) = 8.

Multiplying these values, 4 * 4 * 4 * 8 yields 512 which as 512(mod 99) equals 17.

Posted by brianjn on 2008-08-13 21:55:25