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Two sequences \(A=\{a_0, a_1, a_2,\ldots\}\) and\( B=\{b_0,b_1,b_2,\ldots\}\) are defined as follows: \(\[a_0=0, ~a_1=1, ~a_n= a_{n-1} +b_{n-2} \hspace{2mm}\text{for}\hspace{2mm} n\ge2\]\[b_0=1, ~b_1=2, ~b_n=a_{n-2} +b_{n-1}\hspace{2mm}\text{for}\hspace{2mm} n\ge2\] \)What is the remainder when \(a_{50}+b_{50}\) is divided by 5?

 Jun 24, 2018
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I got it!

 Jun 24, 2018

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