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Argentina National Olympiad
2020 Argentina National Olympiad
4
4
Part of
2020 Argentina National Olympiad
Problems
(1)
a not prime if (5a^4 + a^2)/(b^4 + 3b^2 + 4) is an integer
Source: 2020 Argentina OMA L3 p4
12/26/2020
Let
a
a
a
and
b
b
b
be positive integers such that
5
a
4
+
a
2
b
4
+
3
b
2
+
4
\frac{5a^4 + a^2}{b^4 + 3b^2 + 4}
b
4
+
3
b
2
+
4
5
a
4
+
a
2
is an integer. Show that
a
a
a
is not prime.
prime
Integer
number theory