Cubical

Number Theory Level 2

A three-digit number is equal to the sum of the digit cubes. If the digits are $a,b,c$ , then:

$abc = a^3 + b^3 + c^3$

What is the least value of $a+b+c = ?$

Details and Assumptions:

If the digits are $4,6$ and $2$ , then the number should be $462$

The answer is 9.

1 solution

Mahdi Raza
Apr 11, 2020

$\text{There are only four solutions to this equation}: 153,370 \text{ and }407$ $\begin{aligned} 153 &\rightarrow 1 + 5 + 3 = \boxed{9} \\ 370 &\rightarrow 3 + 7 + 0 = 10 \\ 371 &\rightarrow 3 + 7 + 1 = 11 \\ 407 &\rightarrow 4 + 0 + 7 = 11 \end{aligned}$

What formula did you use to get 153 or 370 or 371 or 407

Oussama Seddiki - 1 year, 1 month ago

Cubical

The answer is 9.

1 solution

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