To determine: The smallest nonnegative integer x that satisfies the given system of congruences. x\equiv 6\pmod 8 x\equiv 17\pmod {25}

preprekomW 2021-04-19 Answered
To determine: The smallest nonnegative integer x that satisfies the given system of congruences.
x6±od8
x17±od{25}
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Expert Answer

hajavaF
Answered 2021-04-21 Author has 90 answers
x6±od8
x17±od{25}
We see that the solution x is unique modulo 25.8=200.
Now, 25(1)-8(3)=1.
Thus,
x=6.25(1)-17.8(3)
x=150-408
x=-258
x=58±od{200}
x=142±od{40}
Therefore, x=142.
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