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Byju's Answer
Standard IX
Mathematics
Continued Proportions
Let n=64064...
Question
Let
n
=
640640640643
, without actually computing
n
2
. Prove that
n
2
leave a remainder 1 when
divided by 8.
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Solution
Since 640640640000 is a multiple of 8
643
≡
3
(
m
o
d
8
)
∴
n
=
8
k
+
3
for some positive integer k
∴
n
2
=
64
k
2
+
48
k
+
9
=
1
+
a
multiple of 8
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If
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