a b + c d = a + c b + d Please help me to find a , b , c , d such that a b + c d = a + c b + d ? I take a , b for example 2 , 3 to find c , d but I get stuck on this. I know that is diophantine equation , but I am unable to find suitable a , b , c , d a , b , c , d ∈ Z , a , c ≠ 0Thanks in advance.

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a    b    +      c    d    =            a      +      c              b      +      d      Please help me to find   a  ,  b  ,  c  ,  d such that       a    b    +      c    d    =            a      +      c              b      +      d       ? I take   a  ,  b for example   2  ,  3 to find   c  ,  d but I get stuck on this. I know that is diophantine equation , but I am unable to find suitable   a  ,  b  ,  c  ,  d  a  ,  b  ,  c  ,  d  ∈      Z    ,  a  ,  c  ≠  0Thanks in advance.

driogairea1 · Accepted Answer

This is the best I could get, hope it helps :)            a      b        +            c      d        =                    a        +        c                    b        +        d            For any   h  ,    k  ,    j  ∈      Z    ,    j  ≠  0  ,  h  ≠  −  1Let       {    a    =    k    ,    b    =    j    ,    c    =    −          h      2        −    k    ,    d    =    h    j    }  we get             k      j        −                    h        k            j        =                    k        −                  h          2                k                    h        j        +        j            indeed                     k        −        h        k            j        =                    k        (        1        +        h        )        (        1        −        h        )                    j        (        h        +        1        )            and finally                     k        −        h        k            j        =                    k        (        1        −        h        )            j      Edit.I am not sure that these are ALL the solutions

Alexander Lewis · Accepted Answer

Hint:      a    b    +      c    d    −            a      +      c              b      +      d        =            a              d        2            +              b        2            c              b      d      (      b      +      d      )

Please help me to find a,b,c,d such that a/b+c/d=(a+c)/(b+d)? I take a,b for example 2,3 to find c,d but I get stuck on this. I know that is diophantine equation , but I am unable to find suitable a,b,c,d . a,b,c,d in bbbZ,a,c!=0 Thanks in advance.

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