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Problems
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National and Regional Contests
The Philippines Contests
Philippine MO
2020 Philippine MO
2
2
Part of
2020 Philippine MO
Problems
(1)
Krazy equality
Source: Philippine Mathematical Olympiad 2020/2
1/19/2020
Determine all positive integers
k
k
k
for which there exist positive integers
r
r
r
and
s
s
s
that satisfy the equation
(
k
2
−
6
k
+
11
)
r
−
1
=
(
2
k
−
7
)
s
.
(k^2-6k+11)^{r-1}=(2k-7)^{s}.
(
k
2
−
6
k
+
11
)
r
−
1
=
(
2
k
−
7
)
s
.
algebra
PMO