While every ideal in an algebraic integer ring is generated by two elements, an arbitrary generating set need not contain a two-element generating set

Exhibit an ideal A \subseteq \mathbb{Z} such that A = (a,b,c) but A is not equal to any of (a,b), (a,c), and (b,c).


Consider (6,10,15) = (1), and note that (6,10) = (2), (6,15) = (3), and (10,15) = (5).

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