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4
SMT 2013 Team #4
SMT 2013 Team #4
Source:
February 4, 2013
Problem Statement
For some positive integers
a
a
a
and
b
b
b
,
(
x
a
+
a
b
x
a
−
1
+
13
)
b
(
x
3
+
3
b
x
2
+
37
)
a
=
x
42
+
126
x
41
+
⋯
(x^a+abx^{a-1}+13)^{b}(x^3+3bx^2+37)^{a}=x^{42}+126x^{41}+\cdots
(
x
a
+
ab
x
a
−
1
+
13
)
b
(
x
3
+
3
b
x
2
+
37
)
a
=
x
42
+
126
x
41
+
⋯
. Find the ordered pair
(
a
,
b
)
(a, b)
(
a
,
b
)
.
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