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Mod p2

The sequence {Zk} has period ptN mod p2.

Theorem 5

Given an elliptic divisibility sequence {Zk} then for all m ÎZ

where t = ZN-12 Z2 / ZN-2 mod p

Example

Remember the sequence {Zk} generated by the curve E: y2 + y = x3 - x mod 5 has t=4 and N=8. The same sequence considered mod 52 has period ptN = 160

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