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CentroAmerican
2020 Centroamerican and Caribbean Math Olympiad
6
6
Part of
2020 Centroamerican and Caribbean Math Olympiad
Problems
(1)
Interoceanic numbers
Source: Centroamerican 2020, problem 6
10/28/2020
A positive integer
N
N
N
is interoceanic if its prime factorization
N
=
p
1
x
1
p
2
x
2
⋯
p
k
x
k
N=p_1^{x_1}p_2^{x_2}\cdots p_k^{x_k}
N
=
p
1
x
1
p
2
x
2
⋯
p
k
x
k
satisfies
x
1
+
x
2
+
⋯
+
x
k
=
p
1
+
p
2
+
⋯
+
p
k
.
x_1+x_2+\dots +x_k=p_1+p_2+\cdots +p_k.
x
1
+
x
2
+
⋯
+
x
k
=
p
1
+
p
2
+
⋯
+
p
k
.
Find all interoceanic numbers less than 2020.
number theory
prime factorization