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 Modular Arithmetic

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The Lucas sequence is the sequence 1, 3, 4, 7, 11,... where the first term is 1, the second term is 3 and each term after that is the sum of the previous two terms. What is the remainder when the $100^{th}$ term of the sequence is divided by 8?

 Apr 6, 2021

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 #1
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The Lucas sequence is determined by

\[L_n = \left( \frac{1 + \sqrt{2}}{2} \right)^n + \left( \frac{1 - \sqrt{5}}{2} \right)^n.\]

Using this formula, remainder when the 100th is divided by 8 is 1.

 Apr 6, 2021
 #2
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Sorry, it was incorrect. I have one more try, however.

RiemannIntegralzzz  Apr 6, 2021
 #3
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Are you just copying answers and plugging them in a box to see if they work?

Melody  Apr 6, 2021

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