MathDB
Problems
Contests
National and Regional Contests
India Contests
India EGMO TST
India EGMO 2021 TST
6
6
Part of
India EGMO 2021 TST
Problems
(1)
a^2+b^2-ab is not a square
Source: India EGMO 2021 TST P6
11/18/2021
Let
n
>
2
n>2
n
>
2
be a positive integer and
b
=
2
2
n
b=2^{2^n}
b
=
2
2
n
. Let
a
a
a
be an odd positive integer such that
a
≤
b
≤
2
a
a\le b \le 2a
a
≤
b
≤
2
a
. Show that
a
2
+
b
2
−
a
b
a^2+b^2-ab
a
2
+
b
2
−
ab
is not a square.
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Perfect Square
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