Wait... does this even exist? Part II

Number Theory Level 2

Let

$a^{3}+b^{3}=c^{2}$

$a+b=c$

Where $a$ , $b$ , and $c$ are distinct positive integers. Find the minimum possible value of $a+b+c$ .

4 solutions

Daniel Lim
Mar 20, 2014

Actually, there is a formula for sum of cubes that is $1^3+2^3+3^3+...+n^3 = (1+2+3+...+n)^2$

So we just plug in the smallest three that are $\boxed{1, 2, 3}$

Shreyas Shastry
Mar 22, 2014

1^3+2^3=3^2

1+2=3

so the required numbers are 1,2,3

and their sum is 6

Sunil Pradhan
Mar 21, 2014

1³ + 2³ = (1 + 2)² = 3³

a + b + c = 6

read 1³ + 2³ = (1 + 2)² = 3²

Sunil Pradhan - 7 years, 2 months ago

Arianna Basha
Mar 20, 2014

It's easy as 1-2-3. Literally. The first that I concluded that it were minimum that must mean it Is a pattern and the answer is less than ten.

So tried 2,2,4, forgeting it was not distinct then I tried more distinct numbers such as 1,2,3.

Which was the answer.

Not really much of an solution, but this was going inside of my head.