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National and Regional Contests
Moldova Contests
EGMO TST - Moldova
2023 Moldova EGMO TST
7
7
Part of
2023 Moldova EGMO TST
Problems
(1)
$$|a+3|+b^2+4\cdot c^2-14\cdot b-12\cdot c+55=0.$$
Source: Moldova EGMO TST 2023
2/4/2023
Find all triplets of integers
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
, that verify the equation
∣
a
+
3
∣
+
b
2
+
4
⋅
c
2
−
14
⋅
b
−
12
⋅
c
+
55
=
0.
|a+3|+b^2+4\cdot c^2-14\cdot b-12\cdot c+55=0.
∣
a
+
3∣
+
b
2
+
4
⋅
c
2
−
14
⋅
b
−
12
⋅
c
+
55
=
0.
equation