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Problems
Contests
International Contests
Tournament Of Towns
1993 Tournament Of Towns
(364) 3
(364) 3
Part of
1993 Tournament Of Towns
Problems
(1)
TOT 364 1993 Spring A J3 operation x*(*z) = (x* y)+ z
Source:
6/10/2024
An operation denoted by
∗
*
∗
defines, for each pair of numbers
(
x
,
y
)
(x, y)
(
x
,
y
)
, a number
x
∗
y
x*y
x
∗
y
so that for all
x
,
y
x, y
x
,
y
and
z
z
z
the identities
x
∗
x
=
0
(
1
)
x*x = 0 \,\,\,\,\, (1)
x
∗
x
=
0
(
1
)
and
x
∗
(
∗
z
)
=
(
x
∗
y
)
+
z
(
2
)
x*(*z) = (x* y)+ z \,\,\,\,\, (2)
x
∗
(
∗
z
)
=
(
x
∗
y
)
+
z
(
2
)
hold (
+
+
+
denoting ordinary addition of numbers). Find
1993
∗
1932
1993* 1932
1993
∗
1932
. (G Galperin)
algebra
Operation