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2002 Flanders Junior Olympiad
2
[To be solved] - Challenge Problem: number array
[To be solved] - Challenge Problem: number array
Source:
August 9, 2004
modular arithmetic
Problem Statement
Prove that there are no perfect squares in the array below:
11
111
1111
.
.
.
22
222
2222
.
.
.
33
333
3333
.
.
.
44
444
4444
.
.
.
55
555
5555
.
.
.
66
666
6666
.
.
.
77
777
7777
.
.
.
88
888
8888
.
.
.
99
999
9999
.
.
.
\begin{array}{cccc}11&111&1111&...\\22&222&2222&...\\33&333&3333&...\\44&444&4444&...\\55&555&5555&... \\66&666&6666&...\\77&777&7777&...\\88&888&8888&...\\99&999&9999&...\end{array}
11
22
33
44
55
66
77
88
99
111
222
333
444
555
666
777
888
999
1111
2222
3333
4444
5555
6666
7777
8888
9999
...
...
...
...
...
...
...
...
...
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