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2006 Austria Beginners' Competition
1
a^{2006} + b^{2006} + 1 is divisible by 2006^2
a^{2006} + b^{2006} + 1 is divisible by 2006^2
Source: 2006 Austria Beginners' Competition p1
October 12, 2022
number theory
divisible
Problem Statement
Do integers
a
,
b
a, b
a
,
b
exist such that
a
2006
+
b
2006
+
1
a^{2006} + b^{2006} + 1
a
2006
+
b
2006
+
1
is divisible by
200
6
2
2006^2
200
6
2
?
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