The smallest positive integer x that satisfies x\equiv 3\pmod 5 x\equiv 5\pmod 7 x\equiv 7\pmod 11
illusiia
Answered question
2021-02-20
Answer & Explanation
komunidadO
Skilled2021-02-22Added 86 answers
We know gcd(5,7)=1.
Also, 1=(3)5-2(7).
Thus,
x=5(3)5-3.2(7)
=75-42
Now, let us find the solution for the congruences given below:
We know gcd(35,11)=1.
Also, 1=-5(35)+16(11).
Thus,
x=7(-5)(35)+33(16)(11)
=-1225+5808
=4583
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