Find the NORMALIZED Gaussian factorization of 666. Also, find the number of ways 666 can be written as a sum of 2 integer squares.

nagasenaz 2021-06-04 Answered
Find the NORMALIZED Gaussian factorization of 666. Also, find the number of ways 666 can be written as a sum of 2 integer squares.
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Benedict
Answered 2021-06-05 Author has 108 answers
66=2×3×3×37
=(1+i)(1i)[(1+2i)(12i)]2(1+6i)(16i)
We know N(a+bi)=a2+b2=666.
This looks like a circle equation where the radius is 66625.81.
Thus, a,b < 25.81 as a and b are to be integers.
On close observation, the values of a,b are
(22,15),(-22,15),(22,-15),(-22,-15)
(15,22),(-15,22),(15,-22),(-15,-22)
Therefore, the number of ways in which 666 can be written in sum of 2 integer squares is 8.
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