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N3
Divisibility of power of integer
Divisibility of power of integer
Source:
October 23, 2017
Divisibility
number theory
Problem Statement
Given positive integers
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
such that
a
∣
c
d
a\mid c^d
a
∣
c
d
and
b
∣
d
c
b\mid d^c
b
∣
d
c
. Prove that
a
b
∣
(
c
d
)
m
a
x
(
a
,
b
)
ab\mid (cd)^{max(a,b)}
ab
∣
(
c
d
)
ma
x
(
a
,
b
)
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