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Baltic Way
2018 Baltic Way
20
20
Part of
2018 Baltic Way
Problems
(1)
A divisibility condition and a sum being prime
Source: Baltic Way 2018, Problem 20
11/6/2018
Find all the triples of positive integers
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
for which the number
(
a
+
b
)
4
c
+
(
b
+
c
)
4
a
+
(
c
+
a
)
4
b
\frac{(a+b)^4}{c}+\frac{(b+c)^4}{a}+\frac{(c+a)^4}{b}
c
(
a
+
b
)
4
+
a
(
b
+
c
)
4
+
b
(
c
+
a
)
4
is an integer and
a
+
b
+
c
a+b+c
a
+
b
+
c
is a prime.
number theory
prime numbers