[seqfan] Two tenuously related problems concerning squares

Alonso Del Arte alonso.delarte at gmail.com
Sun Jun 16 18:04:19 CEST 2013


1. Is it always possible to express n^2 as a sum of n distinct Fibonacci
numbers, or at least almost so but allowing two 1s? e.g.,

 1 = 1
 4 = 1 + 3
 9 = 1 + 3 + 5
16 = 1 + 2 + 5 + 8
25 = 1 + 1 + 2 + 8 + 13

2. At the time Howard Eves wrote *Mathematical Reminiscences*, a division
of a 175 x 175 square into 24 smaller squares, none of them equal, was the
record. The interest so far appears to be in using as few smaller squares
as possible. But what I'm curious about is: what is the minimum possible
number of equal squares? For n = 175, that would be 0. But for say, n = 3,
that would be 5, since the 3 x 3 square can be divided into a single 2 x 2
and five 1 x 1s.

Al

-- 
Alonso del Arte
Author at SmashWords.com<https://www.smashwords.com/profile/view/AlonsoDelarte>
Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>


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