A triangle has side lengths a, a and b. It has perimeter P and area A. Given that b and P are integers, and that P is numerically equal to A^2, find all possible pairs (a, b).
This problem comes from British Maths Olympiad Round 1 in 2020.
This is a 3½-hour paper with 6 problems taken by students in their own schools. Selection is based on performance in the UK Senior Mathematical Challenge (UKSMC). Students achieving a certain score in UKSMC and eligible to represent the UK at the IMO are entered automatically for BMO 1. Typically 1300 students sit BMO 1. A team of around 25 markers gathers in December to mark all the scripts over a 3-day period. The top 100 students receive prizes.
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