这个不定冠词的用法正确吗?（a topic for an interesting research paper）

这个不定冠词的用法正确吗?（a topic for an interesting research paper）
Can you think of an idea for (a) topic for an interesting research paper?
上句中,a topic 是否应该修正为 the topic (for an interesting research paper)?
还有这句：After the man standing over there was punched in the nose,he suffered (a) bloody nose.
是否应该改成 (the) bloody nose?