Are there any size constraints on the reduced solutions $x$, $(0<x<q)$, to $x^p\equiv 1\mod q$, for $p$ and $q$ specific primes? (Considering the primitive $p$-th roots of unity modulo $q$).

I can see that $x>q^{1/p}$ as $x^p>q$. Also for $p=2$, the solutions are simply $\pm 1$. Besides these, can anything be said so far about the lower or upper bounds?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.