Solve the system of congruence's x-=1(mod 3), x-=4(mod 5), x-=6(mod 7)

Brennan Flores 2021-02-03 Answered
Solve the system of congruences
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Expert Answer

timbalemX
Answered 2021-02-04 Author has 108 answers

Step 1
Systems of linear congruences may be solved using methods from linear algebra: Matrix inversion, Cramer's rule. In case the modulus is prime, everything we know from linear algebra goes over to systems of linear congruences
Step 2
Consider the system of congruence
x1(mod3)
x4(mod5)
x6(mod7)
Try a solution of the form
x=35a+37b+57c
Taking the remainders mod 3,5, and 7. It gives the three equations
135c2cc(mod3)
421bb(mod5)
615aa(mod7)
a=6,b=4,c=1
One solution is therefore
x=356+374+57(1)=139(mod105)=34

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