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2011 239 Open Mathematical Olympiad
1
a+b=b(a-c), c+1 square of prime, then a+b of ab square
a+b=b(a-c), c+1 square of prime, then a+b of ab square
Source: 239 2011 J2
May 17, 2020
number theory
Problem Statement
Positive integers
a
,
b
,
c
a,b,c
a
,
b
,
c
satisfy that
a
+
b
=
b
(
a
ā
c
)
a+b=b(a-c)
a
+
b
=
b
(
a
ā
c
)
and c+1 is a square of a prime. Prove that
a
+
b
a+b
a
+
b
or
a
b
ab
ab
is a square.
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