Solution to x^k=b mod m Using Prime Factors and Mod Congruence

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Let m be a product of distinct primes p1,p2,...pr.
Assume x=c (mod pi) is a solution of x^k=b (mod pi) for all i =1,2,3,...r.
Can I conclude that x=c (mod m) is a solution of x^k=b (mod m) ?

(I think that if a=b mod x and a=b mod y then a=b mod(xy), provided that gcd(x,y)=1)
 
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lifom said:
Can I conclude that x=c (mod m) is a solution of x^k=b (mod m) ?

Yes.
 

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