8 Sep
2003
8 Sep
'03
3:19 a.m.
Can someone characterize the integer solutions to: ad + bc + bd = ac These correspond to pairs of complex numbers (a+bi)(c+di) such that the real part (ac-bd) is equal to the imaginary part (ad+bc). In Pari; { for (a=1,50, for (b=1,50, for (c=1,50, for (d=1,50, if (a*d+b*c+b*d==a*c,print(a","b","c","d)))))) } gives (e.g.) 10,8,9,1 10,8,18,2 10,8,27,3 10,8,36,4 10,8,45,5 Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com