9 Sep
2003
9 Sep
'03
10:55 a.m.
At 07:52 AM 9/8/03, Jon Perry wrote:
Can you explain the integer solutions when the real part is equal to 2*the imaginary part +1.
In other words, you want to find integers a,b,c,d such that (a + bi)(c + di) = (2k + 1) + ki for some integer k. This has integer solutions iff gcd(a,b) = 1 and 2a+b is not a multiple of 5. (The latter condition is equivalent to saying that a+bi is not a Gaussian integer multiple of 2+i.) The corresponding values of k are the solutions to (2a + b)k == -a (mod a^2 + b^2). Not very enlightening, really. -- Fred W. Helenius <fredh@ix.netcom.com>