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MathLinks Contest 4th
6.1
0461 number theory 4th edition Round 6 p1
0461 number theory 4th edition Round 6 p1
Source:
May 7, 2021
number theory
4th edition
Problem Statement
Find all positive integers
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
, such that the following equality takes place for an infinity of positive integers
n
n
n
(
1
a
+
2
a
+
.
.
.
+
n
a
)
b
=
(
1
c
+
2
c
+
.
.
.
+
n
c
)
d
(1^a + 2^a +...+ n^a)^b = (1^c + 2^c +...+ n^c)^d
(
1
a
+
2
a
+
...
+
n
a
)
b
=
(
1
c
+
2
c
+
...
+
n
c
)
d
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