



 
This is not a dumb question. I would start by writing the squares of the ten digits 0, 1, 2, ... , 9. What is the units digit of each square? Did you get every possible digit? Can you get a different digit if you square a larger integer? Suppose $n$ is an integer and $d$ is its units digit. There is an integer $k$ so that \[n = k \times 10 + a.\] For example $165976 = 16597 \times 10 + 6.$ The square of $n$ can then be written \[n^2 = \left(k \times 10 + d\right)^{2}.\] Expanding the right side and simplifying I get \[n^2 = k^2 \times 100 + 2dk \times 10 + d^{2}.\] I hope this helps, 



Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 