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Vojtěch Jarník IMC
1999 VJIMC
Problem 2
11|a^n+b^n -> 11|a,11|b for all a,b, find n
11|a^n+b^n -> 11|a,11|b for all a,b, find n
Source: VJIMC 1999 1.2
August 1, 2021
number theory
Problem Statement
Find all natural numbers
n
≥
1
n\ge1
n
≥
1
such that the implication
(
11
∣
a
n
+
b
n
)
⟹
(
11
∣
a
∧
11
∣
b
)
(11\mid a^n+b^n)\implies(11\mid a\wedge11\mid b)
(
11
∣
a
n
+
b
n
)
⟹
(
11
∣
a
∧
11
∣
b
)
holds for any two natural numbers
a
a
a
and
b
b
b
.
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