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2017 Polish Junior Math Olympiad Finals
1.
1.
Part of
2017 Polish Junior Math Olympiad Finals
Problems
(1)
2017 Polish Junior Math Olympiad Finals P1
Source: 2017 Polish Junior Math Olympiad Finals
5/22/2023
Let
a
a
a
,
b
b
b
, and
c
c
c
be positive integers for which the number
a
2
+
b
b
2
+
c
\frac{a\sqrt2+b}{b\sqrt2+c}
b
2
+
c
a
2
+
b
is rational. Show that the number
a
b
+
b
c
+
c
a
ab+bc+ca
ab
+
b
c
+
c
a
is divisible by
a
+
b
+
c
a+b+c
a
+
b
+
c
.
number theory