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Selection and Training Session

Belarus algebra

Problem

Find all sequences of positive integers satisfying the equality a) for all ; b) for all .
Solution
a) there are no such sequences;

b) there exists a unique sequence: , for all .
Final answer
a) No such sequences exist. b) The unique sequence is a1 = 1, a2 = 1, and ai = 2 for all i at least 3.

Techniques

Recurrence relationsIntegers