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BMT Problems
2021 BMT
11
11
Part of
2021 BMT
Problems
(2)
BMT 2021 Guts Round p11
Source:
10/7/2022
Compute the sum of all prime numbers
p
p
p
with
p
≥
5
p \ge 5
p
≥
5
such that
p
p
p
divides
(
p
+
3
)
p
−
3
+
(
p
+
5
)
p
−
5
(p + 3)^{p-3} + (p + 5)^{p-5}
(
p
+
3
)
p
−
3
+
(
p
+
5
)
p
−
5
. .
number theory
BMT 2021 General p11
Source:
9/27/2023
Compute the number of sequences of five positive integers
a
1
,
.
.
.
,
a
5
a_1,..., a_5
a
1
,
...
,
a
5
where all
a
i
≤
5
a_i \le 5
a
i
≤
5
and the greatest common divisor of all five integers is
1
1
1
.
number theory