Suppose $b$ and $c$ are positive integers.

When $b^2$ is written in base $c$, the result is $121_c$. When $c^2$ is written in base $b$, the result is $71_b$.

What is $b+c$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Suppose $b$ and $c$ are positive integers.

When $b^2$ is written in base $c$, the result is $121_c$. When $c^2$ is written in base $b$, the result is $71_b$.

What is $b+c$?
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<|im_start|>assistant

user
17
Suppose $b$ and $c$ are positive integers.

When $b^2$ is written in base $c$, the result is $121_c$. When $c^2$ is written in base $b$, the result is $71_b$.

What is $b+c$?
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