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4.1
System of equations on integers
System of equations on integers
Source: Belarus TST 2024
July 17, 2024
algebra
system of equations
number theory
Problem Statement
Six integers
a
,
b
,
c
,
d
,
e
,
f
a,b,c,d,e,f
a
,
b
,
c
,
d
,
e
,
f
satisfy:
{
a
c
e
+
3
e
b
d
−
3
b
c
f
+
3
a
d
f
=
5
b
c
e
+
a
c
f
−
a
d
e
+
3
b
d
f
=
2
\begin{cases} ace+3ebd-3bcf+3adf=5 \\ bce+acf-ade+3bdf=2 \end{cases}
{
a
ce
+
3
e
b
d
−
3
b
c
f
+
3
a
df
=
5
b
ce
+
a
c
f
−
a
d
e
+
3
b
df
=
2
Find all possible values of
a
b
c
d
e
abcde
ab
c
d
e
D. Bazyleu
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