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MagicMathMaster
MIT's Floor Function Integral Becomes the Dirichlet Eta Function: number theory & infinite series
A remarkable 2026 MIT Integration Bee Quarterfinals problem where an infinite sum of floor functions transforms into divisor counting, perfect-square parity, a telescoping series, and finally the Dirichlet eta function. The key observation is that the divisor-counting function is odd exactly when its input is a perfect square. That converts a ...
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