MathDB
Problems
Contests
International Contests
Austrian-Polish
1990 Austrian-Polish Competition
4
4
Part of
1990 Austrian-Polish Competition
Problems
(1)
x_i4 + 14x_ix_{i+1} + 1 = y_i^4, diophantine system
Source: Austrian - Polish 1990 APMC
5/7/2020
Find all solutions in positive integers to:
{
x
1
4
+
14
x
1
x
2
+
1
=
y
1
4
x
2
4
+
14
x
2
x
3
+
1
=
y
2
4
.
.
.
x
n
4
+
14
x
n
x
1
+
1
=
y
n
4
\begin{cases} x_1^4 + 14x_1x_2 + 1 = y_1^4 \\ x_2^4 + 14x_2x_3 + 1 = y_2^4 \\ ... \\ x_n^4 + 14x_nx_1 + 1 = y_n^4 \end{cases}
⎩
⎨
⎧
x
1
4
+
14
x
1
x
2
+
1
=
y
1
4
x
2
4
+
14
x
2
x
3
+
1
=
y
2
4
...
x
n
4
+
14
x
n
x
1
+
1
=
y
n
4
system of equations
number theory
Diophantine equation
diophantine