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National and Regional Contests
Czech Republic Contests
District Round (Round II)
2009 District Round (Round II)
1
1
Part of
2009 District Round (Round II)
Problems
(1)
Czech republic,district round,2009,problem 1
Source:
2/18/2012
given a 4-digit number
(
a
b
c
d
)
10
(abcd)_{10}
(
ab
c
d
)
10
such that both
(
a
b
c
d
)
10
(abcd)_{10}
(
ab
c
d
)
10
and
(
d
c
b
a
)
10
(dcba)_{10}
(
d
c
ba
)
10
are multiples of
7
7
7
,having the same remainder modulo
37
37
37
.find
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
.
modular arithmetic
number theory proposed
number theory