The Present Pyramid

Algebra Level 2

Mr. Tumnas is replacing Santa Claus in 2014 and so he will be delivering box presents to the world! He wants to organize his presents by stacking them in a Present Pyramid. He starts with 10,000 presents on the bottom. On the next layer, he has 9,801 presents. On the next layer, he has 9,604, on the next layer he has 9409 presents, and on and on, so that he has 1 present at the top of the pyramid. In total, Mr. Tumnas has N presents in the pyramid where N is an integer. The greatest prime factor of N is Y. What is the value of Y?

Details and Assumptions: The Present Pyramid will not topple over; and after Mr. Tumnas completes the pyramid, there are no more presents left over.

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