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Bulgaria National Olympiad
2017 Bulgaria National Olympiad
4
4
Part of
2017 Bulgaria National Olympiad
Problems
(1)
all triples (p,a,m) satisfying a condition
Source: Bulgarian NMO 2017, 3rd round, p.4
4/21/2017
Find all triples (p,a,m); p is a prime number,
a
,
m
∈
N
a,m\in \mathbb{N}
a
,
m
∈
N
, which satisfy:
a
≤
5
p
2
a\leq 5p^2
a
≤
5
p
2
and
(
p
−
1
)
!
+
a
=
p
m
(p-1)!+a=p^m
(
p
−
1
)!
+
a
=
p
m
.
algebra
number theory