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India IOQM
2024-25 IOQM India
10
IOQM P10 2024
IOQM P10 2024
Source:
September 8, 2024
calculus
integration
Problem Statement
Determine the number of positive integral values of
p
p
p
for which there exists a triangle with sides
a
,
b
,
a,b,
a
,
b
,
and
c
c
c
which satisfy
a
2
+
(
p
2
+
9
)
b
2
+
9
c
2
−
6
a
b
−
6
p
b
c
=
0.
a^2 + (p^2 + 9)b^2 + 9c^2 - 6ab - 6pbc = 0.
a
2
+
(
p
2
+
9
)
b
2
+
9
c
2
−
6
ab
−
6
p
b
c
=
0.
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