You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
是否存在实系数非常数多项式 P(x),Q(x)，使得P(x)^{10}+P(x)^9=Q(x)^{21}+Q(x)^{20}?
让我们一步一步地思考。请以“Answer: \boxed{<final_answer>}”的格式输出最终答案。如果是选择题，请按顺序输出正确的选项，不带任何标点或空格。对于其他类型的问题，请只输出最终答案的数值。
user
0
rule
是否存在实系数非常数多项式 P(x),Q(x)，使得P(x)^{10}+P(x)^9=Q(x)^{21}+Q(x)^{20}?
让我们一步一步地思考。请以“Answer: \boxed{<final_answer>}”的格式输出最终答案。如果是选择题，请按顺序输出正确的选项，不带任何标点或空格。对于其他类型的问题，请只输出最终答案的数值。
train