MathDB
Problems
Contests
National and Regional Contests
Moldova Contests
EGMO TST - Moldova
2021 Moldova EGMO TST
8
x(x+1)(x+2)(x+3)=1679^{p-1}+1680^{p-1}+1681^{p-1}
x(x+1)(x+2)(x+3)=1679^{p-1}+1680^{p-1}+1681^{p-1}
Source: Moldova EGMO TST 2021
February 4, 2023
number theory
Problem Statement
Find all pairs of nonnegative integers
(
x
,
p
)
(x, p)
(
x
,
p
)
, where
p
p
p
is prime, that verify
x
(
x
+
1
)
(
x
+
2
)
(
x
+
3
)
=
167
9
p
−
1
+
168
0
p
−
1
+
168
1
p
−
1
.
x(x+1)(x+2)(x+3)=1679^{p-1}+1680^{p-1}+1681^{p-1}.
x
(
x
+
1
)
(
x
+
2
)
(
x
+
3
)
=
167
9
p
−
1
+
168
0
p
−
1
+
168
1
p
−
1
.
Back to Problems
View on AoPS