Can anyone explain how ? This is just using the substitution described above.
Hello All,
I was working on problems involving relatively prime quadratic integers. Here is the one that has me miffed.
Assume that for relatively prime quadratic integers in . From here, it can be shown that for some unit and some quadratic integer in .
Could someone help explain how that statement is true?
Well there's non-elegant brute force,
Gaussian Divisors of an Integer - Wolfram Demonstrations Project
Haven't actually run the numbers. Of course there should be a better way, but for this few divisors, it wouldn't be so bad. And possibly a pattern would emerge allowing one to generalize and see the better solution.
Well I downloaded the .nb file and opened it up in Mathematica, enabled the scale, but I'm still confused on how we determine 2 of them that are relatively prime and meet the other condition.
From what I see, we get values of 1,2,4,8, and 16. Am I missing something? None of these are relatively prime to one another.