Let and be sequences of positive reals such that, and for all . Then k . (k should be the maximum possible value).
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Multiplying the recurrence, we have a n + 1 b n + 1 = 1 + a n b n + 4 a n b n 1 ≥ 2 . This implies that a n b n > n + 1 for all n ∈ N so max ( a 2 0 1 8 , b 2 0 1 8 ) > 2 0 1 9 > 4 4 .