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Rioplatense Mathematical Olympiad, Level 3
2000 Rioplatense Mathematical Olympiad, Level 3
4
4
Part of
2000 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
a,b,c positive integers, a^2 + b^2 + 1 = c^2, prove [a/2] + [c / 2] is even
Source: Rioplatense Olympiad 2000 level 3 P4
9/6/2018
Let
a
,
b
a, b
a
,
b
and
c
c
c
be positive integers such that
a
2
+
b
2
+
1
=
c
2
a^2 + b^2 + 1 = c^2
a
2
+
b
2
+
1
=
c
2
. Prove that
[
a
/
2
]
+
[
c
/
2
]
[a/2] + [c / 2]
[
a
/2
]
+
[
c
/2
]
is even.Note:
[
x
]
[x]
[
x
]
is the integer part of
x
x
x
.
number theory
positive integers
Integer Part
Even