In a certain street, there are more than fifty but less than five hundred houses in a row, numbered from 1, 2, 3 etc. consecutively. There is a house in the street, the sum of all the house numbers on the left side of which is equal to the sum of all house numbers on its right side. Find the number of this house.
Also find all solutions to this problem, without the above 50 and 500 constraint. Try to find a method to solve this without guess and check.

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