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Austrian MO Beginners' Competition
2002 Austria Beginners' Competition
1
1
Part of
2002 Austria Beginners' Competition
Problems
(1)
product of sum of seven consecutive pairs
Source: 2002 Austria Beginners' Competition p1
10/4/2022
We calculate the sum of
7
7
7
natural consecutive pairs (e.g.
2
+
4
+
6
+
8
+
10
+
12
+
14
2+4+6+8+10+12+14
2
+
4
+
6
+
8
+
10
+
12
+
14
) and we will call the result
A
A
A
, then the sum of the next
7
7
7
consecutive pairs (in the example,
16
+
18
+
.
.
.
16+ 18+...
16
+
18
+
...
) and its result we will call
B
B
B
, and finally we calculate the sum of the following
7
7
7
consecutive pairs and its result we will call
C
C
C
. Can the product
A
B
C
ABC
A
BC
be
200
2
3
2002^3
200
2
3
?
number theory
algebra