I'm looking for solution to a problem to calculate modulo of very large number that can contain 25000 digits or less (n) with 10 digit number (m). ( n % m ) ?
Pointer to appropriate theory resource is also welcome.
Thanks
2026-03-26 04:31:26.1774499486
How to calculate modulo of large integer (number having 25000 digits)
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As small as your modulus is, I don't think you can do significantly better than ordinary long division (typically done in base $2^{64}$) to compute the remainder.
However, you can optimize the individual steps; e.g. by using an algorithm like Barrett reduction to obtain the remainder of a 2 digit x 1 digit remainder calculation.
Writing efficient (or even simply correct) division code is a very irritating task; unless you really, really like this sort of programming or are using a specialized algorithm for a very special case, you are certainly better off with a good (or even just decent) bignum package.