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Kvant 2019
M2574
M2574
Part of
Kvant 2019
Problems
(1)
x^n +y^n modulo n^2
Source: Kvant Magazine No. 9 2019 M2574
3/14/2023
Let
n
>
1
n>1
n
>
1
be a positive integer. Show that the number of residues modulo
n
2
n^2
n
2
of the elements of the set
{
x
n
+
y
n
:
x
,
y
∈
N
}
\{ x^n + y^n : x,y \in \mathbb{N} \}
{
x
n
+
y
n
:
x
,
y
∈
N
}
is at most
n
(
n
+
1
)
2
\frac{n(n+1)}{2}
2
n
(
n
+
1
)
. [I]Proposed by N. Safaei (Iran)
number theory
Kvant