Possible Last Digits of Triangular Numbers

All possible last digits of triangular numbers are derived in the table.
\[n\]
\[n-1\]
\[n(n-1)\]
\[\frac{n}{2}(n-1)\]
0 1 0 0, 5
1 2 2 1, 6
2 3 6 3, 8
3 4 2 1, 6
4 5 0 0, 5
5 6 0 0, 5
6 7 2 1, 6
7 8 6 3, 8
8 9 2 1, 6
9 0 0 0, 5
By exhaustion the only possible last digits of a triangular number are 0, 1, 3, 5, 6, or 8,

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