The key to the problem is the fact f(k-1)*f(k)=f(k^2)
(k^2-k+1)(k^2+k+1)=k^4+k^2+1
Which means
f(k)^2/f(k^2)=f(k)/f(k-1)
So if we rewrite the inequality in the problem as
2019 >= f(1)^2/f(1^2) * f(2)^2/f(2^2) *... * f(n)^2/f(n^2)
Each individual term reduces
2019 >= f(1)/f(0) * f(2)/f(1) * ...* f(n)/f(n-1)
And most of the terms cancel out leaving
2019 >= f(n)/f(0) = f(n)
2019 >= n^2 + n + 1
n <= 44
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Posted by Jer
on 2019-04-19 10:33:24 |
Better solution
