If a_0=1, a_1=1 and a_n=a_ n-1 a_ n-2 +1, n>2, then

JEE Advanced Mathematics question

If , and , , then

(A) is odd, is even
(B) is even, is odd
(C)both are oddCorrect
(D)both are even

Answer: (C)

Solution

Take the recurrence for (see note). Only parities matter. Use odd·odd odd and anything·even even, then add 1: - : odd, odd; - : odd = even; - : even = odd; - : even = odd; - : odd = even; - and

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Question ID VK-110083