parmenides51 31.05.2020 11:39 The last four digits of a perfect square are equal. Prove that all of them are zeros.
Prod55 19.02.2021 23:19 Suppose that $f^2=a_1a_2....a_krrrr_{10}$ and $r\neq 0$. Obviously $r=1,4,5,6,9$ and $10^4|f^2-r\cdot1111\Rightarrow f^2\equiv 7r\pmod {16}$ But $f^2=0,1,4,9\pmod {16}$ and $7r\equiv 7,12,3,10,15\pmod {16}$ etc