Check if a solution exist for a linear congruence with possible zero variable












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(AX + B) mod D = C




I changed it form to AX ≡ (C-B) mod D then try to find if GCD(A,D)|(C-B) if so then a solution exist, but I think this method yields some false result when handling some zeros in it.



Is there any special case that must I know if I want to check if a linear congruence has a solution or not if there can be a one or more zero exist in the equation ?
Example : A and B could be zero, etc.






elementary-number-theory modular-arithmetic







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    0












    $begingroup$



    (AX + B) mod D = C




    I changed it form to AX ≡ (C-B) mod D then try to find if GCD(A,D)|(C-B) if so then a solution exist, but I think this method yields some false result when handling some zeros in it.



    Is there any special case that must I know if I want to check if a linear congruence has a solution or not if there can be a one or more zero exist in the equation ?
    Example : A and B could be zero, etc.






    elementary-number-theory modular-arithmetic







    share|cite|improve this question









    $endgroup$















      0












      0








      0


      1



      $begingroup$



      (AX + B) mod D = C




      I changed it form to AX ≡ (C-B) mod D then try to find if GCD(A,D)|(C-B) if so then a solution exist, but I think this method yields some false result when handling some zeros in it.



      Is there any special case that must I know if I want to check if a linear congruence has a solution or not if there can be a one or more zero exist in the equation ?
      Example : A and B could be zero, etc.






      elementary-number-theory modular-arithmetic







      share|cite|improve this question









      $endgroup$





      (AX + B) mod D = C




      I changed it form to AX ≡ (C-B) mod D then try to find if GCD(A,D)|(C-B) if so then a solution exist, but I think this method yields some false result when handling some zeros in it.



      Is there any special case that must I know if I want to check if a linear congruence has a solution or not if there can be a one or more zero exist in the equation ?
      Example : A and B could be zero, etc.






      elementary-number-theory modular-arithmetic




      elementary-number-theory modular-arithmetic






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 15 at 4:48









      Andrean LayAndrean Lay

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