OFFSET
1,3
COMMENTS
Row sums are:
{0, 2, 12, 6, 20, 0, 12, 32, 16, 40, 0}.
Modulo ten they are:
{0, 2, 2, 6, 0, 0, 2, 2, 6, 0, 0}.
The block:
{0},
{0, 2},
{0, 6, 6},
{0, 2, 0, 4},
{0, 0, 8, 4, 8},
{0, 0, 0, 0, 0, 0},
shows up in three places.
Only even {0,2,4,6,8} show up.
It may be a field representation, but can you get the
original tables back from it?
FORMULA
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].
EXAMPLE
{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, 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}
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn,uned
AUTHOR
Roger L. Bagula and Gary W. Adamson, Sep 19 2008
STATUS
approved