perplexus.info :: Numbers : A false conjecture

A false conjecture (Posted on 2017-01-27)

"Every positive number bigger than 1 can be represented as a sum of a square, a nonnegative cube and two positive Fibonacci numbers".
Example: 113=100+0+5+8

NOT SO!

Find the smallest integer n justifying the title of this puzzle.

Rem: It is quite a big number!

See The Solution Submitted by Ady TZIDON

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Subject	Author	Date
Who cares about the correct answer?	Ady TZIDON	2017-02-25 10:05:23
re: I found it!	Ady TZIDON	2017-02-25 09:58:37
I found it!	Brian Smith	2017-01-29 13:49:28
re(2): computer attempt	Daniel	2017-01-29 13:12:03
re(2): computer attempt	Ady TZIDON	2017-01-27 21:53:53
re: computer attempt	Charlie	2017-01-27 14:24:25
computer attempt	Charlie	2017-01-27 12:37:47

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