You are responsible for keeping your receipt.
And here are excerpts from the warranty:
Apple reserves the right to change the method by which Apple may provide warranty service to you, and your Apple Product’s eligibility to receive a particular method of service. Service will be limited to the options available in the country where service is requested. Service options, parts availability and response times may vary according to country. You may be responsible for shipping and handling charges if the Apple Product cannot be serviced in the country it is in. If you seek service in a country that is not the country of purchase, you will comply with all applicable import and export laws and regulations and be responsible for all custom duties, V.A.T. and other associated taxes and charges. For international service, Apple may repair or replace Apple Products and parts with comparable Apple Products and parts that comply with local standards.
And this is from the AppleCare terms:
To receive service or support under the Plan, you agree to comply with the following:
(i) Provide your Plan Agreement Number and a copy of your Plan’s original proof of purchase, if requested;
And:
The terms of the Plan, including the original sales receipt of the Plan and the Plan Confirmation, prevail over any conflicting, additional, or other terms of any purchase order or other document, and constitute your and Apple’s entire understanding with respect to the Plan.