To determine: The smallest nonnegative integer x that satisfies the given system of congruences. x\equiv 1\pmod 4 x\equiv 8\pmod 9

shadsiei 2021-03-10 Answered
To determine: The smallest nonnegative integer x that satisfies the given system of congruences.
x1±od4
x8±od9
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Expert Answer

falhiblesw
Answered 2021-03-12 Author has 97 answers
x1±od4
x8±od9
We see that the solution x is unique modulo 9.4=36.
Now, 9(1)-4(2)=1.
Thus,
x=1.9(1)-8.4(2)
x=9-64
x=-55
x=19±od{36}
x=17±od{36}
Therefore, x=17.
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