Last Digits Using Binomial Expansion

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Last Digits Using Binomial Expansion

## Formula

If:

$$N=a+b$$

and $$b$$ is divisible by $10^k$, then:

$$N^n\equiv a^n\pmod{10^k}$$

## Usage

- Used to determine the last $$k$$ digits of large powers when a convenient binomial decomposition is available.

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