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National and Regional Contests
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India IOQM
2024-25 IOQM India
13
IOQM P13 2024
IOQM P13 2024
Source:
September 8, 2024
Problem Statement
Three positive integers
a
,
b
,
c
a,b,c
a
,
b
,
c
with
a
>
c
a>c
a
>
c
satisfy the following equations :
a
c
+
b
+
c
=
b
c
+
a
+
66
,
a
+
b
+
c
=
32
ac + b+c = bc + a + 66, \; \; \; \; a+b+c=32
a
c
+
b
+
c
=
b
c
+
a
+
66
,
a
+
b
+
c
=
32
Find the value of
a
a
a
.
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