Number Theory

Question

0

26

1

+594

In base $b,$ the square of the number $17_b$ is $211_b$. Find the base $b$.

onyuIee Aug 27, 2024

Maxematics · Answer 1 · 2024-08-27T10:37:59

$b + 7 = 2b^2+b+1$

$2b^2 = 6$

$b^2 = 3$

$\mathbf{b = \sqrt{3}}$

But since sqrt(3) < 7, the base wouldn't work for the left side of the equation. Therefore, there is no solution.