Cube which is One Less than a Square
Jump to navigation
Jump to search
Theorem
$8$ is the only cube number which is $1$ less than a square:
- $2^3 + 1 = 3^2$
Proof
This is a specific instance of 1 plus Perfect Power is not Prime Power except for 9.
$\blacksquare$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $8$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $8$