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show that the ring of integers of K = Q(isqrt(d)), for d = 1, 2, 3, 7, 11, 19, 43, 67, 163, is principal.

i) for the first five values of d, the ring is Euclidean for the norm.

ii) for d = 19, 43, 67, 143, the integer n = N((1 + isqrt(d)) / 2) is prime and the prime numbers less and equal than n are inert in K.

iii) check that every ideal of norm less than 2sqrt(d) / pi is principal and finish the proof

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