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2022 China Team Selection Test
4
Diophantine equation is back
Diophantine equation is back
Source: 2022 China TST, Test 4 P4
April 30, 2022
Diophantine equation
number theory
Problem Statement
Find all positive integers
a
,
b
,
c
a,b,c
a
,
b
,
c
and prime
p
p
p
satisfying that
2
a
p
b
=
(
p
+
2
)
c
+
1.
2^a p^b=(p+2)^c+1.
2
a
p
b
=
(
p
+
2
)
c
+
1.
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