PUMaC 2024 · 数论（B 组） · 第 5 题

PUMaC 2024 — Number Theory (Division B) — Problem 5

Let σ be a permutation of the set S := { 1 , 2 , . . . , 100 } , such that σ ( a + b ) ≡ σ ( a ) + σ ( b ) (mod 100) whenever a, b, a + b ∈ S . Denote by f ( s ) the sum of the distinct values σ ( s ) can take over all possible σ s satisfying the given condition. What is the nonnegative difference between the maximum and minimum value f takes on when ranging over all s ∈ S ?

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