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EGMO TST - Moldova
2023 Moldova EGMO TST
4
4
Part of
2023 Moldova EGMO TST
Problems
(1)
2m-n+13p=2072,\\3m+11n+13p=2961.
Source: Moldova EGMO TST 2023
2/4/2023
Find all triplets of prime numbers
(
m
,
n
,
p
)
(m, n, p)
(
m
,
n
,
p
)
, that satisfy the system of equations:
{
2
m
−
n
+
13
p
=
2072
,
3
m
+
11
n
+
13
p
=
2961.
\left\{\begin{matrix} 2m-n+13p=2072,\\3m+11n+13p=2961.\end{matrix}\right.
{
2
m
−
n
+
13
p
=
2072
,
3
m
+
11
n
+
13
p
=
2961.
number theory
prime numbers
algebra
system of equations