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partial sum of consecutive integers


Does a natural number n exist such that 1+2+3+4+...+n is a three-digit number with identical digits?

Adapted from Mathematics Teacher(1990). March Calendar; Problem 16, p207.


 Extensions

Does a natural number n exist such that 1+2+3+4+...+n is a 4-digit, 5-digit, ... number with identical digits?



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