In congruence classes ZmZ, reduce the equation am⋅xm2=cm either by finding convenient representation for amandbm or by using the inverse of am. Then find a solution for this congruence directly or by replacing cm : with its appropriate representative in ZmZ. If there is no solution explain why. Here am,bm,xm(=x),cm∈ZmZ: InZ19Z,[2]⋅x2=[13]:

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In congruence classes ZmZ, reduce the equation am⋅xm2=cm either by finding convenient representation for amandbm or by using the inverse of am. Then find a solution for this congruence directly or by replacing cm : with its appropriate representative in ZmZ. If there is no solution explain why. Here am,bm,xm(=x),cm∈ZmZ:  InZ19Z,[2]⋅x2=[13]:

gotovub · Accepted Answer

Step 1 Let y=x2 then the given congruence relation becomes, ay≡b mod mt i^s2y≡13mod19 This congruence has unique solution if and only if gcd(a,m)=1 Here gcd(2,19)=1 hence the given congruence has unique solution. Now since 2 has an inverse, we get y≡2−113mod19 which is the only solution. The inverse of 2∈Z19 is 10. y≡130mod19⇒y=16 Now y=x2⇒16=42. Hence x =4 is the required solution.

In congruence classes Z/(mZ), reduce the equation a_m*x_m^2=c_m either by finding convenient representation for a_m and b_m or by using the inverse of

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