y - Institute for Building Materials - ETH Zürich

Applet
x i+1
Square test
Theorem of Marsaglia g
x
(1968)
For a congruential generator the random
numbers b i in an n-cube cube-test b t ttest t li lie on parallel ll l
n-1 n 1 1 dimensional dimensional hyperplanes.
∃ a a a x + a x + + a x p =
1 1,..., , , n : ( 1 i 2 i + 1 ... n i + n n− 1 ) mod p 0
proof using:
∃∀ pcn , , at least one set
a a,..., a :
( 1
n )
1 ... ) n
ac + + a c mod p =
1 n p
1
0
n
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