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  3. Project Euler #110: Diophantine reciprocals II

Project Euler #110: Diophantine reciprocals II

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This problem is a programming version of Problem 110 from projecteuler.net

In the following equation are positive integers.

It can be verified that when = 1260 there are 113 distinct solutions and this is the least value of for which the total number of distinct solutions exceeds one hundred.

What is the least value of for which the number of distinct solutions ?

Input Format

A single line containing one number ,

Output Format

The number the answer to a problem.

Sample Input

113

Sample Output

1260

Author

bayleef

Difficulty

Easy

Max Score

100

Submitted By

295

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