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National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2020 Junior Balkan Team Selection Tests - Moldova
5
JBMO TST Moldova Problem 5
JBMO TST Moldova Problem 5
Source:
October 14, 2020
number theory
Problem Statement
Let there be
A
=
1
a
1
2
a
2
…
10
0
a
1
00
A=1^{a_1}2^{a_2}\dots100^{a_100}
A
=
1
a
1
2
a
2
…
10
0
a
1
00
and
B
=
1
b
1
2
b
2
…
10
0
b
1
00
B=1^{b_1}2^{b_2}\dots100^{b_100}
B
=
1
b
1
2
b
2
…
10
0
b
1
00
, where
a
i
,
b
i
∈
N
a_i , b_i \in N
a
i
,
b
i
∈
N
,
a
i
+
b
i
=
101
−
i
a_i + b_i = 101 - i
a
i
+
b
i
=
101
−
i
, (
i
=
1
,
2
,
…
,
100
i= 1,2,\dots,100
i
=
1
,
2
,
…
,
100
). Find the last 1124 digits of
P
=
A
∗
B
P = A * B
P
=
A
∗
B
.
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