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2019 Silk Road
3
3
Part of
2019 Silk Road
Problems
(1)
\varphi (a ^ n + n) = 2 ^ n , euler function diophantine
Source: SRMC 2019 P3
7/16/2019
Find all pairs of
(
a
,
n
)
(a, n)
(
a
,
n
)
natural numbers such that
φ
(
a
n
+
n
)
=
2
n
.
\varphi (a ^ n + n) = 2 ^ n.
φ
(
a
n
+
n
)
=
2
n
.
(
φ
(
n
)
\varphi (n)
φ
(
n
)
is the Euler function, that is, the number of integers from
1
1
1
up to
n
n
n
, relative prime to
n
n
n
)
number theory
Eulers function
relatively prime
Diophantine equation