+0

# natural numbers

0
59
1

Solve the following equation, where a, b, and c are natural numbers.

$$a + \frac{1}{b + \frac{1}{c}} = \frac{10}{7}$$

Feb 27, 2021

Since $a,b,c$ all have to be natural numbers, $a=1$ because it must be less than $\frac{10}{7}$, but also an integer greater than $0$. Furthermore, we now have $$\frac{1}{b+\frac{1}{c}} = \frac{3}{7}$$ $$\frac{c}{bc+1} = \frac{3}{7}$$. Therefore, we find that $c=3$ and $b=2$. Thus, our answer is $(a,b,c) = \boxed{(1,2,3)}.$