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1964 All Russian Mathematical Olympiad
051
ASU 051 All Russian MO 1964 10.2 a-k^n is divisible by b-k
ASU 051 All Russian MO 1964 10.2 a-k^n is divisible by b-k
Source:
June 18, 2019
number theory
Problem Statement
Given natural
a
,
b
,
n
a,b,n
a
,
b
,
n
. It is known, that for every natural
k
k
k
(
k
≠
b
k\ne b
k
=
b
) the number
a
−
k
n
a-k^n
a
−
k
n
is divisible by
b
−
k
b-k
b
−
k
. Prove that
a
=
b
n
a=b^n
a
=
b
n
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