PUMaC 2025 · 代数（A 组） · 第 6 题

PUMaC 2025 — Algebra (Division A) — Problem 6

Let c be a real number, and let f ( t ) = ( t − 0 . 01) + ( t − c ) i for every real number t . Suppose that m ( t ) is a (not necessarily continuous) function from R to C such that 1 2 m ( t ) + 1 + = ( t − 1)( t + 1) 2 m ( t ) for every real number t . Over all such functions f ( t ) and m ( t ), what is the maximum possible number of distinct ordered pairs of real numbers ( a, b ) such that f ( a ) = m ( b )? 1

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