2016 is absolutely awesome 17

Number Theory Level 5

F 1 = F 2 = 1 ; F n + 2 = F n + 1 + F n , n ≥ 1 F_1=F_2=1; F_{n+2}=F_{n+1}+F_n,\,n\ge1

Find the smallest integer k k such that the 4 last digits of F k F_k is 2016.

This is a part of the Set .


The answer is 1068.

Khang Nguyen Thanh by Khang Nguyen Thanh , 27, Vietnam

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1 solution

Tran Hieu
Dec 28, 2015

Using Excel, computed G n = ( G n − 1 + G n − 2 ) mod 10000 G_n = (G_{n-1}+G_{n-2})\text{ mod }10000 for first 2000 n, find out that G n = 2016 where n = 1068 G_n = 2016 \text{ where }n = \boxed{1068} .

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Can you post a non-CS approach?

Pi Han Goh - 5 years, 5 months ago

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@Pi Han Goh Could you post one instead please??

Aaghaz Mahajan - 2 years, 9 months ago

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