User:Bilal Raza

product of two integers m and b congruent to 1 at modulo prime n Theorem:- If n is any prime then for every positive integer m<n their exist positive integer b<n : 'm*b=1(mod n). Proof:- Let n is any prime and m is positive integer less then n. we known all integer less then any prime n number are co-prime to n that's way we can able to write (m,n)=1      where 1 is greatest common divisor of m and n        we also known from number theory that greatest common divisor of ant two integers can be        written as combination of that numbers, therefore their exist s,t belong to integers : 1=ms+tn this implies       1-ms=tn this implies       n|(1-ms) this implies       ms=1(mod n) now if sn then we can take b=s(mod n) which will give the same result so                 bm=1(mod n) hence prove.