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Greece National Olympiad
1991 Greece National Olympiad
4
1^{1990}+2^{1990}+3^{1990}+...+1990^{1990} mod 10
1^{1990}+2^{1990}+3^{1990}+...+1990^{1990} mod 10
Source: 1991 Greece MO Grade XII p4
September 6, 2024
number theory
remainder
Problem Statement
If we divide number
1
1990
+
2
1990
+
3
1990
+
.
.
.
+
199
0
1990
1^{1990}+2^{1990}+3^{1990}+...+1990^{1990}
1
1990
+
2
1990
+
3
1990
+
...
+
199
0
1990
with
10
10
10
, what remainder will we find?
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