<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Consider the positive integer

$$
n=2^{r}-16^{s}
$$

where \( r \) and \( s \) are also positive integers. Find the conditions that \( r \) and \( s \) must satisfy for the remainder of the division of \( n \) by 7 to be 5. Determine the smallest number that meets this condition. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
768
Consider the positive integer

$$
n=2^{r}-16^{s}
$$

where \( r \) and \( s \) are also positive integers. Find the conditions that \( r \) and \( s \) must satisfy for the remainder of the division of \( n \) by 7 to be 5. Determine the smallest number that meets this condition.
test