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Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2022 Latvia Baltic Way TST
P16
P16
Part of
2022 Latvia Baltic Way TST
Problems
(1)
Two expressions are powers of a prime
Source: Latvian TST for Baltic Way 2022 P16
11/24/2022
Find all triples of positive integers
(
a
,
b
,
p
)
(a,b,p)
(
a
,
b
,
p
)
, where
p
p
p
is a prime, such that both
a
+
b
a+b
a
+
b
and
a
b
+
1
ab+1
ab
+
1
are some powers of
p
p
p
(not necessarily the same).
number theory