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UKMT Junior Mathematical Olympiad, 2025

Number theory Difficulty 3.0 AMC 10/12 Prove it United Kingdom

In this diagram, there are three squares. The larger white square has side length $a$ cm and the smaller one has side length $b$ cm, and $a$ and $b$ are both integers. The shaded area is $286 \text{ cm}^2$ .

(a) Find one possible value for $a$ . No explanation is needed. [2 points]

(b) Find another possible value for $a$ . No explanation is needed. [4 points]

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