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Balkan MO Shortlist
2015 Balkan MO Shortlist
N4
N4
Part of
2015 Balkan MO Shortlist
Problems
(1)
a,b relative prime and divide x^3 + y^3 => (a+b - 1) divides (x^3+y^3)
Source: Balkan BMO Shortlist 2015 N4
8/5/2019
Find all pairs of positive integers
(
x
,
y
)
(x,y)
(
x
,
y
)
with the following property: If
a
,
b
a,b
a
,
b
are relative prime and positive divisors of
x
3
+
y
3
x^3 + y^3
x
3
+
y
3
, then
a
+
b
ā
1
a+b - 1
a
+
b
ā
1
is divisor of
x
3
+
y
3
x^3+y^3
x
3
+
y
3
.(Cyprus)
number theory
relatively prime
Divisibility