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1992 All Soviet Union Mathematical Olympiad
564
ASU 564 Commonwealth of Independent States 1991 (1+x)(1+x^2)(1+x^4)=1+y^7
ASU 564 Commonwealth of Independent States 1991 (1+x)(1+x^2)(1+x^4)=1+y^7
Source:
August 15, 2019
system of equations
algebra
Problem Statement
Find all real
x
,
y
x, y
x
,
y
such that
{
(
1
+
x
)
(
1
+
x
2
)
(
1
+
x
4
)
=
1
+
y
7
(
1
+
y
)
(
1
+
y
2
)
(
1
+
y
4
)
=
1
+
x
7
\begin{cases}(1 + x)(1 + x^2)(1 + x^4) = 1+ y^7 \\ (1 + y)(1 + y^2)(1 + y^4) = 1+ x^7 \end{cases}
{
(
1
+
x
)
(
1
+
x
2
)
(
1
+
x
4
)
=
1
+
y
7
(
1
+
y
)
(
1
+
y
2
)
(
1
+
y
4
)
=
1
+
x
7
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