Mathematical_Recreations-Kraitchik-2e

162 Mathematical Recreations
can determine how many nonequivalent regular magic
squares of a particular prime order p there are. In Figure
38 are given the four nonequivalent panmagic squares of
order 5 from which all others can be derived by certain
permutations of rows and columns.
2. REGULAR SQUARES OF ODD COMPOSITE ORDER m. Relatively
few modifications are required to apply the proce-
18 24 5 6
10 11 17 23
22 3 9 15
14 20 21 2
1 7 13 19
12
4
16
8
25
15 18 21 4 7
24 2 10 13 16
8 11 19 22 5
17 25 3 6 14
1 9 12 20 23
20 22 4 6
9 11 18 25
23 5 7 14
12 19 21 3
1 8 15 17
13
2
16
10
24
13 17 21 5 9
25 4 8 12 16
7 11 20 24 3
19 23 2 6 15
1 10 14 18 22
FIGURE 38. Basic Panmagic Squares of Order 5.
dures for generating magic squares of odd prime order to
squares of odd composite order. Essentially they may be
expressed by changing the restriction "divisible by p" to
"not prime to m." Thus a lattice
(x, y) = (a, b) + ret, u) + s(v, w)
will cover every cell of the fundamental square if tw - U1)
is prime to m, and the resulting square will be at least