I know the answer to this already: the possible values of the tens digit are 1, 3, 5, 7, and 9. But I don't know how to prove it, can someone help please? Thanks!
2026-03-25 21:54:03.1774475643
The units digit of a perfect square is 6. What are the possible values of the tens digit?
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Suppose $$n=\sum_i a_i10^i$$ Then $$n^2\equiv 20a_1a_0+a_0^2\pmod{100}$$ Setting $a_0=6$, this becomes $20a_1+36$. With the choices of $a_1$ we obtain $1,3,5,7,9$ as desired.