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Baltic Way
2021 Baltic Way
16
No NoN-Null iNts
No NoN-Null iNts
Source: Baltic Way 2021, Problem 16
November 15, 2021
number theory
number theory proposed
Problem Statement
Show that no non-zero integers
a
a
a
,
b
b
b
,
x
x
x
,
y
y
y
satisfy
{
a
x
−
b
y
=
16
,
a
y
+
b
x
=
1.
\begin{cases} a x - b y = 16,\\ a y + b x = 1. \end{cases}
{
a
x
−
b
y
=
16
,
a
y
+
b
x
=
1.
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