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%I #2 Oct 12 2012 14:54:52
%S 0,0,2,0,6,6,0,2,0,4,0,0,8,4,8,0,0,0,0,0,0,0,2,6,2,0,0,2,0,6,6,0,8,0,
%T 6,6,0,2,0,4,4,0,2,0,4,0,0,8,4,8,0,0,8,4,8,0,0,0,0,0,0,0,0,0,0,0
%N A triangular sequence "representation" of the modulo 10 Integer field: t(+)(n,m)=Mod[n + m, 10]; t(x)(n,m)=Mod[n*m, 10]; t(n,m)=Mod[t(=)(n,m)*t(X)(n,m),10].
%C Row sums are:
%C {0, 2, 12, 6, 20, 0, 12, 32, 16, 40, 0}.
%C Modulo ten they are:
%C {0, 2, 2, 6, 0, 0, 2, 2, 6, 0, 0}.
%C The block:
%C {0},
%C {0, 2},
%C {0, 6, 6},
%C {0, 2, 0, 4},
%C {0, 0, 8, 4, 8},
%C {0, 0, 0, 0, 0, 0},
%C shows up in three places.
%C Only even {0,2,4,6,8} show up.
%C It may be a field representation, but can you get the
%C original tables back from it?
%F t(+)(n,m)=Mod[n + m, 10]; t(x)(n,m)=Mod[n*m, 10]; t(n,m)=Mod[t(=)(n,m)*t(X)(n,m),10].
%e {0},
%e {0, 2},
%e {0, 6, 6},
%e {0, 2, 0, 4},
%e {0, 0, 8, 4, 8},
%e {0, 0, 0, 0, 0, 0},
%e {0, 2, 6, 2, 0, 0, 2},
%e {0, 6, 6, 0, 8, 0, 6, 6},
%e {0, 2, 0, 4, 4, 0, 2, 0, 4},
%e {0, 0, 8, 4, 8, 0, 0, 8, 4, 8},
%e {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
%t Clear[t1, t2, t, n, m, a]; t1[n_, m_] = Mod[n + m, 10]; t2[n_, m_] = Mod[n*m, 10]; t[n_, m_] = Mod[t1[n, m]*t2[n, m], 10]; a = Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]
%K nonn,uned
%O 1,3
%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 19 2008
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