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