equation for integers











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ok here is the problem. suppose i want to find all pair of a and b such that a*b=10, let's this was first equation in our system and now i need some second equation, such that after putting it into the system, system should only return all integer pair of solutions.



so i have two question: do this kind of equation exist, if so what is it and second , can i generalize all this stuff (for example with the given arbitrary equation with n unknown can i write down some second equation and in "solutions intersection" all solutions be only integers) ?










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    up vote
    -1
    down vote

    favorite












    ok here is the problem. suppose i want to find all pair of a and b such that a*b=10, let's this was first equation in our system and now i need some second equation, such that after putting it into the system, system should only return all integer pair of solutions.



    so i have two question: do this kind of equation exist, if so what is it and second , can i generalize all this stuff (for example with the given arbitrary equation with n unknown can i write down some second equation and in "solutions intersection" all solutions be only integers) ?










    share|cite|improve this question


























      up vote
      -1
      down vote

      favorite









      up vote
      -1
      down vote

      favorite











      ok here is the problem. suppose i want to find all pair of a and b such that a*b=10, let's this was first equation in our system and now i need some second equation, such that after putting it into the system, system should only return all integer pair of solutions.



      so i have two question: do this kind of equation exist, if so what is it and second , can i generalize all this stuff (for example with the given arbitrary equation with n unknown can i write down some second equation and in "solutions intersection" all solutions be only integers) ?










      share|cite|improve this question















      ok here is the problem. suppose i want to find all pair of a and b such that a*b=10, let's this was first equation in our system and now i need some second equation, such that after putting it into the system, system should only return all integer pair of solutions.



      so i have two question: do this kind of equation exist, if so what is it and second , can i generalize all this stuff (for example with the given arbitrary equation with n unknown can i write down some second equation and in "solutions intersection" all solutions be only integers) ?







      systems-of-equations diophantine-equations






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      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Nov 23 at 11:59









      Harry Peter

      5,43111439




      5,43111439










      asked Nov 18 at 17:03









      d4ta l0l

      203




      203



























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