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KEAM 2019 Math Paper
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© examsnet.com
Question : 63
Total: 121
The remainder when
2
2003
is divided by 17 is
7
8
2
1
0
Validate
Solution:
We have,
2
2000
=
(
2
4
)
500
=
(
17
−
1
)
500
=
500
C
0
17
500
−
500
C
1
17
499
+
.
.
.
−
500
C
499
17
+
(
−
1
)
500
17
m
+
1
, where
m
is some positive integer
=
2
2003
=
(
8
)
(
2
2000
)
=
8
(
17
m
+
1
)
=
17
(
8
m
)
+
8
1
Hence, the remainder will be 8 .
© examsnet.com
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