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Eotvos Mathematical Competition (Hungary)
1936 Eotvos Mathematical Competition
3
x +1/2 (x + y - 1)(x + y- 2) = a
x +1/2 (x + y - 1)(x + y- 2) = a
Source: Eotvos 1936 p3
September 10, 2024
number theory
Problem Statement
Let
a
a
a
be any positive integer. Prove that there exists a unique pair of positive integers
x
x
x
and
y
y
y
such that
x
+
1
2
(
x
+
y
−
1
)
(
x
+
y
−
2
)
=
a
.
x +\frac12 (x + y - 1)(x + y- 2) = a.
x
+
2
1
(
x
+
y
−
1
)
(
x
+
y
−
2
)
=
a
.
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