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CCA Math Bonanza
2022 CCA Math Bonanza
T1
Minimizing Exponents
Minimizing Exponents
Source:
April 27, 2022
Problem Statement
Let
a
a
a
,
b
b
b
,
c
c
c
, and
d
d
d
be positive integers such that
7
7
a
⋅
63
7
b
=
14
3
c
⋅
4
9
d
77^a \cdot 637^b = 143^c \cdot 49^d
7
7
a
⋅
63
7
b
=
14
3
c
⋅
4
9
d
. Compute the minimal value of
a
+
b
+
c
+
d
a+b+c+d
a
+
b
+
c
+
d
.2022 CCA Math Bonanza Team Round #1
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