Largest Number not Expressible as Sum of Multiples of 23 and 28/Historical Note

Historical Note on Largest Number not Expressible as Sum of Multiples of 23 and 28

Wilhelm Fliess thought he had stumbled upon a remarkable fact about the numbers $23$ and $28$: that combinations of them could be used to explain practically every earthly phenomenon.

From this "discovery" be built the pseudoscience of biorhythms.

However, it needs to be noted that all but a finite set of positive integers can be represented in the form $23 x + 28 y$ for positive integers $x$ and $y$.

The number $593$ is the largest which cannot.

Every pair of coprime integers has the same property as $23$ and $28$.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $593$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $593$