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Albania JBMO TST
2015 Albania JBMO TST
3
Find the remainder of division of $(m+3)^{1444}$ to $n$
Find the remainder of division of $(m+3)^{1444}$ to $n$
Source: Albania JTST 2015
October 4, 2023
Problem Statement
1
1
⋅
2
+
1
2
⋅
3
+
1
3
⋅
4
+
⋯
+
1
2014
⋅
2015
=
m
n
,
\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\dots+\frac{1}{2014\cdot2015}=\frac{m}{n},
1
⋅
2
1
+
2
⋅
3
1
+
3
⋅
4
1
+
⋯
+
2014
⋅
2015
1
=
n
m
,
where
m
n
\frac{m}{n}
n
m
is irreducible. a) Find
m
+
n
.
m+n.
m
+
n
.
b) Find the remainder of division of
(
m
+
3
)
1444
(m+3)^{1444}
(
m
+
3
)
1444
to
n
n{}
n
.
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