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6
Isn't a perfect square!
Isn't a perfect square!
Source:
February 4, 2015
quadratics
Problem Statement
If
a
a
a
,
b
b
b
,
c
c
c
,
d
d
d
are integers and
A
=
2
(
a
−
2
b
+
c
)
4
+
2
(
b
−
2
c
+
a
)
4
+
2
(
c
−
2
a
+
b
)
4
A=2(a-2b+c)^4+2(b-2c+a)^4+2(c-2a+b)^4
A
=
2
(
a
−
2
b
+
c
)
4
+
2
(
b
−
2
c
+
a
)
4
+
2
(
c
−
2
a
+
b
)
4
,
B
=
d
(
d
+
1
)
(
d
+
2
)
(
d
+
3
)
+
1
B=d(d+1)(d+2)(d+3)+1
B
=
d
(
d
+
1
)
(
d
+
2
)
(
d
+
3
)
+
1
, then prove that
(
A
+
1
)
2
+
B
\left (\sqrt{A}+1 \right )^2 +B
(
A
+
1
)
2
+
B
cannot be a perfect square.
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