MathDB
Problems
Contests
National and Regional Contests
India Contests
India IOQM
2022-23 IOQM India
8
IOQM 2022-23 P-8
IOQM 2022-23 P-8
Source:
October 30, 2022
number theory
prime numbers
IOQM
Problem Statement
Suppose the prime numbers
p
p
p
and
q
q
q
satisfy
q
2
+
3
p
=
197
p
2
+
q
q^2+3p=197p^2+q
q
2
+
3
p
=
197
p
2
+
q
.Write
p
q
\frac{p}{q}
q
p
as
l
+
m
n
l+\frac{m}{n}
l
+
n
m
, where
l
,
m
,
n
l,m,n
l
,
m
,
n
are positive integers ,
m
<
n
m<n
m
<
n
and
G
C
D
(
m
,
n
)
=
1
GCD(m,n)=1
GC
D
(
m
,
n
)
=
1
. Find the maximum value of
l
+
m
+
n
l+m+n
l
+
m
+
n
.
Back to Problems
View on AoPS