1894 Brewer’s / N / nth, or nth plus One
in University slang, means to the utmost degree. Thus, Cut to the nth means wholly unnoticed by a friend. The expression is taken from the index of a mathematical formula, where n stands for any number, and n + 1, one more than any number.
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Entry taken from Dictionary of Phrase and Fable, edited by the Rev. E. Cobham Brewer, LL.D. and revised in 1895.