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Thread: Solving Conguence

  1. #1
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    Solving Conguence

    I am in trouble and unable to understand congruence for below , please help me to solve one one example for understanding.
    Solving Conguence-1.jpg
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  2. #2
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    Re: Solving Conguence

    You can try all the possible values for x to see whether the congruence holds

    (a)(i)
    Put x=0,1,2,3,4,5
    2x^2+3x+1\equiv 1,0,3,4,3,0\pmod{6}
    x\equiv 1,5\pmod{6}
    (ii)
    Put x=0,1,2,3,...,10
    x^3-3x^2+2\equiv 2,0,9,2,7,8,0,0,3,4,9\pmod{11}
    x\equiv 1,6,7\pmod{11}

    factorize the polynomial may help but you have to solve it carefully
    2x^2+3x+1\equiv (2x+1)(x+1)\equiv 0\pmod{6}
    There are 4 conditions:
    2x+1\equiv 0\pmod{6}
    x+1\equiv 0\pmod{6}
    2x+1\equiv 2\pmod{6},x+1\equiv 3\pmod{6}
    2x+1\equiv 3\pmod{6},x+1\equiv 2\pmod{6}
    Thanks from Archie
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  3. #3
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    Re: Solving Conguence

    The second is more straightforward to solve by factorising because it is \pmod{11} and 11 is prime.
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