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Soros Olympiad in Mathematics
VI Soros Olympiad 1999 - 2000 (Russia)
9.4
diophantine with products (VI Soros Olympiad 1990-00 R2 9.4)
diophantine with products (VI Soros Olympiad 1990-00 R2 9.4)
Source:
May 28, 2024
number theory
Diophantine equation
diophantine
Problem Statement
Are there integers
k
k
k
and
m
m
m
for which
(
k
−
3
)
(
k
−
2
)
(
k
−
1
)
k
+
1
(
k
+
1
)
(
k
+
2
)
(
k
+
3
)
(
k
+
4
)
+
1
=
m
(
m
+
1
)
+
(
m
+
1
)
(
m
+
2
)
+
(
m
+
2
)
m
?
\frac{(k-3)(k-2)(k-1)k+1}{(k+1)(k+2)(k+3)(k+4)+1}=m(m+1)+(m+1)(m+2)+(m+2)m \,\, ?
(
k
+
1
)
(
k
+
2
)
(
k
+
3
)
(
k
+
4
)
+
1
(
k
−
3
)
(
k
−
2
)
(
k
−
1
)
k
+
1
=
m
(
m
+
1
)
+
(
m
+
1
)
(
m
+
2
)
+
(
m
+
2
)
m
?
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