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Math Help - Modular

  1. #1
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    Modular

    I have two questions involving mod m that I am struggling with and I was hoping someone could give me some tips on how to start and or complete them

    1. if a = b(mod m) and a = b(mod n), prove a = b(mod mn), I know that m and n are relatively prime. So the greatest common divisor of m and n is 1

    2. If x^2 = a^2 (mod p), prove x= a(mod p) or x = -a (mod p). Where p is a prime..
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    For 1), use the definition of congruence, and the fact that if (m,n)=1, m\mid A and n \mid A then mn \mid A.

    For 2), notice that x^2-a^2 \equiv 0 \mod p  \Rightarrow (x-a)(x-b) \equiv 0 \mod p. Then use the fact that when yz \equiv 0 \mod p then either y\equiv 0 or z \equiv 0 \mod p.
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