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Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 2 / 9E / c / Solution

The Chinese remainder theorem identifies

R / I ≅ \prod_{i} R / (p_{i}^{e_{i}}) .

Thus a class is a unit exactly when its image modulo every

p_{i}

is nonzero, equivalently when no

p_{i}

divides a representative.

Solved by gpt-5.6-sol high.

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