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2022 Turkey Junior National Olympiad
3
3
Part of
2022 Turkey Junior National Olympiad
Problems
(1)
Minimum value of exponent in diophantine equation with 4 unknowns
Source: Turkey Junior National Olympiad 2022 P3
12/23/2022
Let
m
,
n
,
a
,
k
m, n, a, k
m
,
n
,
a
,
k
be positive integers and
k
>
1
k>1
k
>
1
such that the equality
5
m
+
63
n
+
49
=
a
k
5^m+63n+49=a^k
5
m
+
63
n
+
49
=
a
k
holds. Find the minimum value of
k
k
k
.
number theory
Diophantine equation