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Diophantine equation with sgn
Diophantine equation with sgn
Source: Poland Math Olympiad 1992 First Round #1
June 2, 2023
number theory
Diophantine equation
Problem Statement
Solve the following equation in real numbers:
(
x
2
−
1
)
(
∣
x
∣
+
1
)
x
+
s
g
n
x
=
[
x
+
1
]
.
\frac{(x^2-1)(|x|+1)}{x+sgnx}=[x+1].
x
+
s
g
n
x
(
x
2
−
1
)
(
∣
x
∣
+
1
)
=
[
x
+
1
]
.
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