Product of two integers a and b (less then integer n) is congruent to 1 if a or b integer is relativity prime to n .

Bézout's Lemma:-
If n is any positive integer then for every positive integer m<n and relatively prime to n then ∃ positive integer b<n : m*b≡1(mod n).

Proof:-
Let n is any positive integer and m is positive integer less then n and 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.