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digits (2a -1)(2b -1) (2c-1)(2d-1) = 2abcd -1 2016 Ecuador NMO (OMEC) 3.5 2.5
digits (2a -1)(2b -1) (2c-1)(2d-1) = 2abcd -1 2016 Ecuador NMO (OMEC) 3.5 2.5
Source:
September 17, 2021
number theory
Digits
Problem Statement
Determine the number of positive integers
N
=
a
b
c
d
‾
N = \overline{abcd}
N
=
ab
c
d
, with
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
nonzero digits, which satisfy
(
2
a
−
1
)
(
2
b
−
1
)
(
2
c
−
1
)
(
2
d
−
1
)
=
2
a
b
c
d
−
1
(2a -1) (2b -1) (2c- 1) (2d - 1) = 2abcd -1
(
2
a
−
1
)
(
2
b
−
1
)
(
2
c
−
1
)
(
2
d
−
1
)
=
2
ab
c
d
−
1
.
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