anonymous
  • anonymous
***
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
oh.. nevermind, ive got it!
ganeshie8
  • ganeshie8
could you pls share the solution
anonymous
  • anonymous
ok, let me type it up

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IrishBoy123
  • IrishBoy123
.
ganeshie8
  • ganeshie8
take ur time :)
anonymous
  • anonymous
But I'm not sure if thats the only solution... can someone help me check pls?
ganeshie8
  • ganeshie8
That looks good! Just for the sake of an alternative : \[\begin{align*} x &\equiv r \pmod{6}, \\ x &\equiv 9 \pmod{20}, \\ x &\equiv 4 \pmod{45} \end{align*}\] From first and second congruence, notice that \(\gcd(6,20)=2\), so it must be the case that \[r\equiv 9\equiv 1\pmod{2}\tag{a}\]. From first and last congruences, notice that \(\gcd(6,45)=3\), so it must be the case that \[r\equiv 4\equiv 1\pmod{3}\tag{b}\] From \((a),~(b)\) it follows \(r\equiv 1\pmod{2\cdot 3}\)
anonymous
  • anonymous
so it is the only solution right?
ganeshie8
  • ganeshie8
Yep! there are no other solutions
anonymous
  • anonymous
ok thank!
ganeshie8
  • ganeshie8
np:)

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