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2020 BMT Fall
18
2020 BMT Individual 18
2020 BMT Individual 18
Source:
January 9, 2022
number theory
Problem Statement
Let
x
x
x
and
y
y
y
be integers between
0
0
0
and
5
5
5
, inclusive. For the system of modular congruences
{
x
+
3
y
≡
1
(
m
o
d
2
)
4
x
+
5
y
≡
2
(
m
o
d
3
)
\begin{cases} x + 3y \equiv 1 \,\,(mod \, 2) \\ 4x + 5y \equiv 2 \,\,(mod \, 3) \end{cases}
{
x
+
3
y
≡
1
(
m
o
d
2
)
4
x
+
5
y
≡
2
(
m
o
d
3
)
, find the sum of all distinct possible values of
x
+
y
x + y
x
+
y
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