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Contests
National and Regional Contests
PEN Problems
PEN A Problems
64
64
Part of
PEN A Problems
Problems
(1)
A 64
Source:
5/25/2007
The last digit of the number
x
2
+
x
y
+
y
2
x^2 +xy+y^2
x
2
+
x
y
+
y
2
is zero (where
x
x
x
and
y
y
y
are positive integers). Prove that two last digits of this numbers are zeros.
quadratics
Divisibility Theory