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Now, we can use property 2 to show that I = (*b*), where (*b*) is the ideal of all elements divisible by *b*. If some *x* in I is not divisible by *b*, then we have *x* = *bq* + *r* and v(*r*) b). On the one hand, *x* – *bq* is in the ideal; on the other hand, *r* is not in the ideal. So we have a contradiction, and *x* is divisible by *b*.

I hope it’s more comprehensible…

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