MathDB
Problems
Contests
National and Regional Contests
Hungary Contests
Eotvos Mathematical Competition (Hungary)
1942 Eotvos Mathematical Competition
2
2
Part of
1942 Eotvos Mathematical Competition
Problems
(1)
ad - bc = + - 1 if ax + by = m and cx + dy = n
Source: Eotvos 1942 p2
9/10/2024
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
and
d
d
d
be integers such that for all integers m and n, there exist integers
x
x
x
and
y
y
y
such that
a
x
+
b
y
=
m
ax + by = m
a
x
+
b
y
=
m
, and
c
x
+
d
y
=
n
cx + dy = n
c
x
+
d
y
=
n
. Prove that
a
d
−
b
c
=
±
1
ad - bc = \pm 1
a
d
−
b
c
=
±
1
.
number theory
system of equations
System
diophantine