Category: Number Theory

Question Number 15787 by tawa tawa last updated on 13/Jun/17 $$\mathrm{Find}\mathrm{the}\mathrm{four}\mathrm{digits}\mathrm{number}\mathrm{such}\mathrm{that}4\cdot \mathrm{abcd}=\mathrm{dcba}$$ Commented by mrW1 last updated on 13/Jun/17 $$\mathrm{I}\mathrm{found}\mathrm{only}4\times 2178=8712$$ Commented by…

Question Number 15742 by RasheedSoomro last updated on 14/Jun/17 $$\mathrm{This}\mathrm{question}\mathrm{is}\mathrm{posted}\mathrm{on}\mathrm{the}\mathrm{request}\mathrm{of}\mathrm{mrW}1$$$$\text{You can't use 'macro parameter character \#' in math mode}$$$$$$$$\mathrm{Find}\mathrm{the}\mathrm{last}\mathrm{last}\mathbf{non}-\mathbf{zero}\mathrm{digit}\mathrm{of}\mathrm{the}\mathrm{expansion}$$$$\mathrm{of}2000!$$ Commented by mrW1 last updated…

Question Number 15377 by Joel577 last updated on 10/Jun/17 $$-39\mathrm{mod}4=?$$ Answered by Tinkutara last updated on 10/Jun/17 $$-39\equiv -3\left(\mathrm{mod}4\right)$$$$\equiv 1\left(\mathrm{mod}4\right)$$$$\mathrm{You}\:\mathrm{can}\:\mathrm{check}:\:−\mathrm{39}\:=\:\mathrm{4}\left(−\mathrm{10}\right)\:+\:\mathrm{1} \…

Question Number 15292 by RasheedSoomro last updated on 09/Jun/17 $$\text{You can't use 'macro parameter character \#' in math mode}$$$$\mathcal{E}\mathrm{xpansion}\mathrm{of}100!\mathrm{has}24,0^{\prime }\mathrm{s}\mathrm{at}\mathrm{the}\mathrm{end}.$$$$\mathrm{Find}\mathrm{the}\mathrm{first}\mathrm{non}-\mathrm{zero}\mathrm{digit}\mathrm{from}\mathrm{right}.$$$$100!=\dots ..\mathrm{d}000\dots 00$$$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{d}?$$ Answered by RasheedSoomro last updated…

Question Number 14757 by RasheedSoomro last updated on 04/Jun/17 $$\mathrm{Solve}:$$$$\frac{1000!}{5\times 10\times 15\times \dots 1000}\equiv \mathrm{x}\left(\mathrm{mod}10\right)$$ Answered by RasheedSoomro last updated on 05/Jun/17 $$\mathrm{x}\equiv \frac{1000!}{5\times 10\times 15\times \dots 1000}(\mathrm{mod}10$$$$\mathrm{x}\equiv\left(\mathrm{1}.\mathrm{2}.\mathrm{3}.\mathrm{4}\right)\left(\mathrm{6}.\mathrm{7}.\mathrm{8}.\mathrm{9}\right)…\left(\mathrm{996}.\mathrm{997}.\mathrm{998}.\mathrm{999}\right)\left(\mathrm{mod}\:\mathrm{10}\right) \…