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2024 Pan-African
1
Number Theory
Number Theory
Source: Pan African Mathematics Olympiad P1
August 15, 2024
PAMO 2024
number theory
Problem Statement
Find all positive intgers
a
,
b
a,b
a
,
b
and
c
c
c
such that
a
+
b
a
+
c
=
b
+
c
b
+
a
\frac{a+b}{a+c}=\frac{b+c}{b+a}
a
+
c
a
+
b
=
b
+
a
b
+
c
and
a
b
+
b
c
+
c
a
ab+bc+ca
ab
+
b
c
+
c
a
is a prime number
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