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Math Help - elementary Number Theory

  1. #1
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    elementary Number Theory

    1-for what values of a(mod 78) will ax is congruence to 26(mod 78) have exactly 13 solutions

    2- given 36x ≡ 42 (mod 42) and 4x ≡ 6 (mod 18
    a) determine the number of solutions to each coungruence equation.
    b) Find integer solutions to each congruence equation
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  2. #2
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    Quote Originally Posted by elole2009 View Post
    for what values of a(mod 78) will ax is congruence to 26(mod 78) have exactly 13 solutions
    Given ax\equiv 26(\bmod 78) let d=\gcd(a,26). It d|26 then there shall be exactly d solutions mod 78. Thus, what are those values of a?
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