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1957 Poland - Second Round
1
\frac{n^5}{120} - \frac{n^3}{24} + \frac{n}{30} is integer
\frac{n^5}{120} - \frac{n^3}{24} + \frac{n}{30} is integer
Source: Polish MO second round 1957 p1
August 29, 2024
number theory
Integer
Problem Statement
Prove that if
n
n
n
is an integer, then
n
5
120
−
n
3
24
+
n
30
\frac{n^5}{120} - \frac{n^3}{24} + \frac{n}{30}
120
n
5
−
24
n
3
+
30
n
is also an integer.
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