Which solution will meet these requirements?

Explanations:

Using Amazon RDS for MySQL introduces additional complexity and latency due to the need for database connections. It may also lead to scalability issues under high load, as RDS can struggle with sudden spikes in traffic. Moreover, using a relational database for this purpose would require careful management of state and locking mechanisms to avoid race conditions.

Amazon DynamoDB is a fully managed NoSQL database that can handle high throughput and scale automatically to accommodate varying loads. By storing the unique identifiers in a DynamoDB table, the Lambda function can efficiently check for duplicates before processing requests. This approach supports high availability and consistent performance, making it suitable for applications with unpredictable request patterns.

While storing unique identifiers in DynamoDB is valid, returning a client error response on duplicate requests does not prevent data inconsistencies or loss. This approach would not allow the application to handle retries gracefully, as the client would have to manage the error response, potentially leading to confusion or data loss in case of retry logic.

Amazon ElastiCache for Memcached provides in-memory caching, but it is not designed for durable storage of request identifiers. If the application receives a duplicate request, the cache may not persist the identifier long enough to effectively handle retries, leading to potential data inconsistencies. Additionally, cache data can be lost on instance failure, which is not acceptable for ensuring consistency across retries.