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Mathematics
General Math
Differences between Gaussian integers with norm 25
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[QUOTE="Ventrella, post: 6011853, member: 310171"] I am exploring Gaussian integers in terms of roots, powers, primes, and composites. I understand that multiplying two integers with norm 5 result in an integer with norm 25. I get the impression that there are twelve unique integers with norm 25, and they come in two flavors: (1) Four of them are 0+5[I]i[/I], 0-5[I]i, [/I]and 5+0i, -5+0i. They lie on the orthogonal (real and imaginary) axes. (2) The other eight are 3+4i, 3-4i, -3+4i, -3-4i, 4+3i, 4-3i, -4+3i and -4-3i. These do not lie on the orthogonal axes. Each of these twelve integers is the product of two integers with norm 5, but it matters which ones. If there are any insights as to these kinds of Gaussian integers (having different symmetries but the same norm), I would appreciate any thoughts. Also, I assume these become more numerous as norms get larger? Thanks! -Jeffrey [/QUOTE]
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Mathematics
General Math
Differences between Gaussian integers with norm 25
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