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Brazil Contests
Brazil National Olympiad
1985 Brazil National Olympiad
5
5
Part of
1985 Brazil National Olympiad
Problems
(1)
Ax + B[x] = Ay + B[y] no solutions except x = y, when A, B reals
Source: Brazilian Mathematical Olympiad 1985 P5
7/27/2018
A
,
B
A, B
A
,
B
are reals. Find a necessary and sufficient condition for
A
x
+
B
[
x
]
=
A
y
+
B
[
y
]
Ax + B[x] = Ay + B[y]
A
x
+
B
[
x
]
=
A
y
+
B
[
y
]
to have no solutions except
x
=
y
x = y
x
=
y
.
algebra
equation