Largest Number Not Expressible as Sum of Fewer than 8 Cubes/Mistake

Source Work

1986: David Wells: Curious and Interesting Numbers:

The Dictionary

$8042$

Mistake

This is probably the largest integer that cannot be represented as the sum of fewer than $8$ cubes.

Correction

$(1) \quad$ This should probably read:

This is probably the largest integer that cannot be represented as the sum of fewer than $7$ cubes

as we have:

$8042 = 1^3 + 4^3 + 4^3 + 10^3 + 10^3 + 10^3 + 17^3$

among many other expressions.

$(2) \quad$ Also note that:

$8042 = 1340^3 + 1338^3 + \paren {-1339}^3 + \paren {-1339}^3 + 2^3$

so what it really ought to say is:

This is probably the largest integer that cannot be represented as the sum of fewer than $7$ positive cubes.

This entry has been excluded from Curious and Interesting Numbers, 2nd ed. of $1997$, so perhaps it was not even true in the first place.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $8042$