help : greatest common factor

xuying1209

For any n,m are intergers, d_n and d_m are divisors of n and m,
respectively. If gcd(n,m)=1, gcd(i,n)=d_n , gcd(j,m)=d_m
sm=1(mod n) , tn=1(mod m),
z=smi+tnj (mod nm)
then gcd(z,nm)=d_nd_m.
I want to know the result is true or false, and how to prove it.

Thanks.

malaygoel

Quote by xuying1209

For any n,m are intergers, d_n and d_m are divisors of n and m,
respectively. If gcd(n,m)=1, gcd(i,n)=d_n , gcd(j,m)=d_m
sm=1(mod n) , tn=1(mod m),
z=smi+tnj (mod nm)
then gcd(z,nm)=d_nd_m.
I want to know the result is true or false, and how to prove it.

Thanks.

I am not sure but the result depends on the value of s and t since they are not unique in a given problem

Similar Threads for: help : greatest common factor
Thread	Forum	Replies
Q factor (Quality Factor)	Introductory Physics Homework	2
what do these have in common	Brain Teasers	2
God = Greatest Common Factor	General Discussion	2
Common static vs common electricity?	General Physics	7

xuying1209	help : greatest common factor Tweet For any n,m are intergers, d_n and d_m are divisors of n and m, respectively. If gcd(n,m)=1, gcd(i,n)=d_n , gcd(j,m)=d_m sm=1(mod n) , tn=1(mod m), z=smi+tnj (mod nm) then gcd(z,nm)=d_nd_m. I want to know the result is true or false, and how to prove it. Thanks.