Counterexample/Examples/Sum of Cubes of Digits

Example of Counterexample

Let $P$ be the statement:

There exists no integer which is the sum of the cubes of its digits.

A counterexample to $P$ is the number $153$, as can be seen in Pluperfect Digital Invariants: $3$ Digits:

\(\ds 153\)

\(=\)

\(\ds 1 + 125 + 27\)

\(\ds \)

\(=\)

\(\ds 1^3 + 5^3 + 3^3\)

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): counterexample
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): counterexample