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Soros Olympiad in Mathematics
VI Soros Olympiad 1999 - 2000 (Russia)
8.5
3x3 NT system a^4+14ab+1=n^4 (VI Soros Olympiad 1990-00 R1 8.5)
3x3 NT system a^4+14ab+1=n^4 (VI Soros Olympiad 1990-00 R1 8.5)
Source:
May 27, 2024
number theory
system of equations
Problem Statement
Solve the following system of equations in natural numbers
{
a
4
+
14
a
b
+
1
=
n
4
b
4
+
14
b
c
+
1
=
m
4
c
4
+
14
c
a
+
1
=
k
4
\begin{cases} a^4+14ab+1=n^4 \\ b^4+14bc+1=m^4 \\ c^4+14ca+1=k^4 \end{cases}
⎩
⎨
⎧
a
4
+
14
ab
+
1
=
n
4
b
4
+
14
b
c
+
1
=
m
4
c
4
+
14
c
a
+
1
=
k
4
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