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National and Regional Contests
India Contests
India National Olympiad
2006 India National Olympiad
2
2
Part of
2006 India National Olympiad
Problems
(1)
n = \frac{1}{2}(a + b - 1)(a + b - 2) + a
Source: Indian National Maths Olympiad, Problem 2
2/5/2006
Prove that for every positive integer
n
n
n
there exists a unique ordered pair
(
a
,
b
)
(a,b)
(
a
,
b
)
of positive integers such that
n
=
1
2
(
a
+
b
−
1
)
(
a
+
b
−
2
)
+
a
.
n = \frac{1}{2}(a + b - 1)(a + b - 2) + a .
n
=
2
1
(
a
+
b
−
1
)
(
a
+
b
−
2
)
+
a
.
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