# McEliece's Theorem (Integer Functions)/Historical Note

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## Historical Note on McEliece's Theorem (Integer Functions)

Donald E. Knuth reports in *The Art of Computer Programming* that this generalisation of Conditions for $\left\lfloor{\log_b x}\right\rfloor$ to equal $\left\lfloor{\log_b \left\lfloor{x}\right\rfloor}\right\rfloor$ was established by Robert James McEliece.

Knuth refers to it (in passing) as **McEliece's Theorem**.

Whiile this name for it is not backed up in the literature, it is convenient for $\mathsf{Pr} \infty \mathsf{fWiki}$, because of its unwieldy nature, to refer to it thus.

## Sources

- 1997: Donald E. Knuth:
*The Art of Computer Programming: Volume 1: Fundamental Algorithms*(3rd ed.) ... (previous) ... (next): $\S 1.2.4$: Integer Functions and Elementary Number Theory: Exercise $34$ (Answers to Exercises)