Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

(a * b)$^{x}$ mod n = ((a$^{x}$ mod n) * (b$^{x}$ mod n)) mod n

Can anyone give me some tips to prove the above equation? Thanks.

share|cite|improve this question

1 Answer 1

This follows from basic modular arithmetic: if $k\equiv r\pmod{n}$ and $\ell\equiv s\pmod{n}$, then $k\ell\equiv rs\pmod{n}$. Since $(ab)^x = a^xb^x$, then what you have is just this instance with $k=a^x$, $\ell=b^x$, $r=a^x\bmod n$ and $s=b^x\bmod n$. The final "$\bmod n$" just assures that you fall inside the main residue class representatives.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.