Dear Colleagues,
As I know, in work
Euler L. (1923) Problema algebraicum ob affectiones prorsus
singulares memorabile / Leonardi Euleri Opera Omnia. Ser.1. Vol.6.
an algebraic formula of a magic square, allowing to construct
magic squares of 4th order from the squared natural numbers, is
presented. For example, if its parameters take the values
p = 2, q = -1, r = 4, s = 8,
d = 0, b = -3, a = 2 and c = -5
Euler formula yields the magic square
169 1764 1 1296
1936 81 484 729
36 361 2304 529
1089 1024 441 676
I ask you to assist me in finding the reference on L.Euler work,
in which he constructs magic squares of 5th order from the squared
natural numbers. I had seen this work before and read even in some
comment that L.Euler found an application of this algebraic formula
in mechanics, but I had lost both references completely.
I need in these references to prepare a new (3rd) edition of my
book "Magic Squares. Number Theory, Algebra, Combinatorial Analysis".
Thank you in advance for any help or advice.
Professor of St-Petersburg
Technical University,
Dr. Yu. V. Chebrakov
Nevsky Ave., Bldg.3, Apt. 11
191186, St-Petersburg, Russia
e-mail: chebra@phdeg.hop.stu.neva.ru