MathDB
Problems
Contests
National and Regional Contests
China Contests
South East Mathematical Olympiad
2021 South East Mathematical Olympiad
7
China South East Mathematical Olympiad 2021 Grade11 P7
China South East Mathematical Olympiad 2021 Grade11 P7
Source:
July 30, 2021
number theory
Euler s totient function
Problem Statement
Determine all the pairs of positive odd integers
(
a
,
b
)
,
(a,b),
(
a
,
b
)
,
such that
a
,
b
>
1
a,b>1
a
,
b
>
1
and
7
φ
2
(
a
)
−
φ
(
a
b
)
+
11
φ
2
(
b
)
=
2
(
a
2
+
b
2
)
,
7\varphi^2(a)-\varphi(ab)+11\varphi^2(b)=2(a^2+b^2),
7
φ
2
(
a
)
−
φ
(
ab
)
+
11
φ
2
(
b
)
=
2
(
a
2
+
b
2
)
,
where
φ
(
n
)
\varphi(n)
φ
(
n
)
is Euler's totient function.
Back to Problems
View on AoPS