Java modular inverse

java modulo inverse
Tony picture Tony · Oct 24, 2011 · Viewed 7.2k times · Source

I'm doing some error correction in Java and to cut a long story short;

Under mod 11:

-4 mod 11 = 7

This I've confirmed by using Google's calculator and a couple of online modulo calculators, but I cannot for the life of me figure out how to do it in Java.

I'm thinking that I need to use an inverse table to find the correct number but I seem to be going round in circles.

Any input would be appreciated.

Thank in advance

Tony

Answer

NPE picture NPE · Oct 24, 2011

The following will compute n mod 11 for any integer n:

(n % 11 + 11) % 11

The result of n % 11 is in the range -10...10. The subsequent addition and the second modulo operation add 11 to n % 11 iff the latter is negative.

This formula works for any base: just replace 11 with another positive integer.

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