# User:Bilal Raza

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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:-**

Letnis any prime andmis positive integer less thenn. we known all integer less then any primennumber are co-prime tonthat's way we can able to write(m,n)=1where 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 exists,tbelong to integers:1=ms+tnthis implies1-ms=tnthis impliesn|(1-ms)this impliesms≡1(mod n)now ifs<nthen we have done. But ifs>nthen we can takeb≡s(mod n)which will give the same result sobm≡1(mod n)hence prove.