p∈Zを素数とする

p = (a + bi + cj + dk)(a' + b'i + c'j + d'k)
= (aa' - bb' - cc' - dd')
+ (ab' + a'b + cd' - c'd)i
+ (ac' + a'c + b'd - bd')j
+ (ad' + a'd + bc' - b'c)k

となるなら

aa' - bb' - cc' - dd' = p
ab' + a'b + cd' - c'd = 0
ac' + a'c + b'd - bd' = 0
ad' + a'd + bc' - b'c = 0

こんなん解けるのか