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Mathematics
Problem
Notice that
11
−
2
=
9
=
3
2
11 - 2 = 9 = 3^2
11
−
2
=
9
=
3
2
and
1111
−
22
=
1089
=
33
2
1111 - 22 = 1089 = 33^2
1111
−
22
=
1089
=
3
3
2
. Show that
(
111111
…
1
)
⏟
2
n
lots of 1
−
(
22222
…
2
)
⏟
n
lots of 2
\underbrace{(111111\dots 1)}_{2n \text{ lots of 1}} - \underbrace{(22222\dots 2)}_{n \text{ lots of 2}}
2
n
lots of 1
(
111111
…
1
)
−
n
lots of 2
(
22222
…
2
)
is a perfect square.
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