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1966 IMO Shortlist
54
54
Part of
1966 IMO Shortlist
Problems
(1)
Soviet Union 11
Source: IMO LongList 1959-1966 Problem 54
9/2/2004
We take
100
100
100
consecutive natural numbers
a
1
,
a_{1},
a
1
,
a
2
,
a_{2},
a
2
,
.
.
.
,
...,
...
,
a
100
.
a_{100}.
a
100
.
Determine the last two digits of the number
a
1
8
+
a
2
8
+
.
.
.
+
a
100
8
.
a_{1}^{8}+a_{2}^{8}+...+a_{100}^{8}.
a
1
8
+
a
2
8
+
...
+
a
100
8
.
number theory
decimal representation
Digits
Last digit
modular arithmetic
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