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Germany Contests
German National Olympiad
2019 German National Olympiad
4
4
Part of
2019 German National Olympiad
Problems
(1)
An old polynomial bijection between N and NxN
Source: Germany 2019, Problem 4
6/20/2019
Show that for each non-negative integer
n
n
n
there are unique non-negative integers
x
x
x
and
y
y
y
such that we have
n
=
(
x
+
y
)
2
+
3
x
+
y
2
.
n=\frac{(x+y)^2+3x+y}{2}.
n
=
2
(
x
+
y
)
2
+
3
x
+
y
.
algebra
polynomial
number theory