Category: Number Theory

Question Number 45439 by Tawa1 last updated on 12/Oct/18 $$\mathrm{Show}\mathrm{that}\mathrm{the}\mathrm{square}\mathrm{of}\mathrm{every}\mathrm{odd}\mathrm{integer}\mathrm{is}\mathrm{of}\mathrm{the}\mathrm{form}8\mathrm{m}+1$$ Answered by tanmay.chaudhury50@gmail.com last updated on 13/Oct/18 $${(2k+1)}^2=4k^2+4k+1$$$$=\mathrm{4}{k}\left({k}+\mathrm{1}\right)+\mathrm{1} \…

Question Number 110895 by Aina Samuel Temidayo last updated on 31/Aug/20 $$\mathrm{How}\mathrm{many}\mathrm{ways}\mathrm{can}2018\mathrm{be}$$$$\mathrm{expressed}\mathrm{as}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{two}\mathrm{squares}?$$ Answered by ajfour last updated on 31/Aug/20 $$\mathrm{43}^{\mathrm{2}} +\mathrm{13}^{\mathrm{2}}…

Question Number 110775 by Aina Samuel Temidayo last updated on 30/Aug/20 $$\mathrm{Let}\mathrm{a},\mathrm{b}\mathrm{and}\mathrm{c}\mathrm{be}\mathrm{positive}\mathrm{integers}\mathrm{such}$$$$\mathrm{that}\mathrm{ab}+1\mid \mathrm{bc}+1\mathrm{and}\mathrm{bc}+1\mid \mathrm{ca}+1.$$$$\mathrm{Show}\mathrm{that}\mathrm{ab}+1\mathrm{is}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{two}$$$$\mathrm{squares}.$$ Terms of Service Privacy Policy…

Question Number 110688 by Aina Samuel Temidayo last updated on 30/Aug/20 $$\mathrm{Let}\mathrm{a},\mathrm{b}\mathrm{and}\mathrm{c}\mathrm{be}\mathrm{positive}\mathrm{integers}\mathrm{such}$$$$\mathrm{that}\mathrm{ab}+1\mid \mathrm{bc}+1\mathrm{and}\mathrm{bc}+1\mid \mathrm{ca}+1.$$$$\mathrm{Show}\mathrm{that}\mathrm{ab}+1\mathrm{is}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{two}$$$$\mathrm{squares}.$$ Terms of Service Privacy Policy…

Question Number 110595 by Aina Samuel Temidayo last updated on 29/Aug/20 $$\mathrm{Evaluate}5!\bullet 6!(\mathrm{mod}7!)$$ Commented by Her_Majesty last updated on 29/Aug/20 $${you}^{\prime }reright$$ Commented…