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Niels Henrik Abels Math Contest (Norwegian Math Olympiad) Final Round
2023 Abelkonkurransen Finale
3a
3a
Part of
2023 Abelkonkurransen Finale
Problems
(1)
Solving 2^a + 5^b + 1 = n! in non-negative integers
Source: 2023 Abelkonkurransen Finale, Problem 3a
3/12/2024
Find all non-negative integers
n
n
n
,
a
a
a
, and
b
b
b
satisfying
2
a
+
5
b
+
1
=
n
!
.
2^a + 5^b + 1 = n!.
2
a
+
5
b
+
1
=
n
!
.
number theory
Diophantine equation