1,381 research outputs found
There are no multiply-perfect Fibonacci numbers
Here, we show that no Fibonacci number (larger than 1) divides the sum of its divisors
Description of Euler bricks using Fibonacci's identity
We show how the Fibonacci's identity is used to obtain Euler bricks. Also,we
put forward the relation between Fibonacci's identity and Euler's formula,
which provides the description of Euler's bricks with noninteger spatial
diagonal. Finally,we establish a relation between the Euler bricks with integer
and noninteger spatial diagonals.Comment: 8 page
The problem of the pawns
In this paper we study the number of ways to place nonattacking
pawns on an chessboard. We find an upper bound for and
analyse its asymptotic behavior. It turns out that
exists and is bounded from above by
. Also, we consider a lower bound for by reducing
this problem to that of tiling an board with square tiles
of size and . Moreover, we use the transfer-matrix
method to implement an algorithm that allows us to get an explicit formula for
for given .Comment: 16 pages; 6 figure
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