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terms of 1,11,111,1111,... base 9 are triangular

Source: ITAMO 1988 p4

February 2, 2020
Triangular numbernumber theory

Problem Statement

Show that all terms of the sequence 1,11,111,1111,...1,11,111,1111,... in base 99 are triangular numbers, i.e. of the form m(m+1)2\frac{m(m+1)}{2} for an integer mm
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