Problem #353

Gaussian factorization
Public 01/20/17 8xp Math 60.9%

Consider the Gaussian integer $ \gamma = 14159 + 71828i $

$ \gamma = (0+i)\times(1+2i)\times(2+3i)\times(5-8i)\times(283-920i) $.
Each factor is a Gaussian prime number.

Can you find the Gaussian factorization of $1415926535897932384626433+7182818284590452353602874i$

Answer format: $a_1,b_1/a_2,b_2/ \dots /a_n,b_n$ where $ a_i \ge 0$ and $a_i$ in ascending order.
To normalize the factors, we must have $ \lvert a_i \rvert \lt \lvert b_i \rvert $

Exemple: $0,1/1,2/2,3/5,-8/283,-920$ for $ \gamma $.

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