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Problem J
Sum of the Year
Proof without words of Nicomachus’s theorem CC BY-SA 3.0 by
Cmglee on
Wikimedia
The year $2025$ has the curious property that
\[ 2025 = (1 + 2 + \dots + 9)^2 = 1^3 + 2^3 + \dots + 9^3. \]Ivan found this to be an intriguing coincidence and wonders how many other such coincidences there are. Can you help him?
Input
The input consists of a single positive integer $n$ ($1 \leq n \leq 1\, 000$).
Output
Output the number of $k$, with $1 \leq k \leq n$, such that
\[ (1 + \dots + k)^2 = 1^3 + \dots + k^3. \]| Sample Input 1 | Sample Output 1 |
|---|---|
1 |
1 |
| Sample Input 2 | Sample Output 2 |
|---|---|
3 |
3 |
