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EGMO TST - Moldova
2021 Moldova EGMO TST
8
8
Part of
2021 Moldova EGMO TST
Problems
(1)
x(x+1)(x+2)(x+3)=1679^{p-1}+1680^{p-1}+1681^{p-1}
Source: Moldova EGMO TST 2021
2/4/2023
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
.
number theory