<ul><li>Casting out nines is a method to find the remainder when a number is divided by 9 by adding all the digits repeatedly.</li><li>Persistence of a number with an operation is the number of times the operation needs to be applied to reach a fixed point.</li><li>The additive persistence of a number is the number of times the digit sum operation needs to be applied before reaching a fixed point.</li><li>Multiplicative persistence involves multiplying digits together, and it is conjectured that this persistence is bounded for all integers.</li></ul>

Additive and multiplicative persistence

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