Junior Mathematical Olympiad 2025 Section A Q1

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 $286$ 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]

(c) Prove that no others are possible. Full explanation is required. [4 points]