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2021 Middle European Mathematical Olympiad
7
Diophantine equation with primes
Diophantine equation with primes
Source: 2021 MEMO T-7
September 5, 2021
number theory
Diophantine equation
memo
MEMO 2021
easy number theorem
Problem Statement
Find all pairs
(
n
,
p
)
(n, p)
(
n
,
p
)
of positive integers such that
p
p
p
is prime and
1
+
2
+
⋯
+
n
=
3
⋅
(
1
2
+
2
2
+
⋅
+
p
2
)
.
1 + 2 + \cdots + n = 3 \cdot (1^2 + 2^2 + \cdot + p^2).
1
+
2
+
⋯
+
n
=
3
⋅
(
1
2
+
2
2
+
⋅
+
p
2
)
.
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