Category: Number Theory

Question Number 112994 by Aina Samuel Temidayo last updated on 10/Sep/20 $$\mathrm{If}\mathrm{n}\mathrm{is}\mathrm{any}\mathrm{even}\mathrm{number},\mathrm{then}$$$$\mathrm{n}({\mathrm{n}}^2+20)\mathrm{is}\mathrm{always}\mathrm{divisible}\mathrm{by}?$$ Answered by mr W last updated on 10/Sep/20…

Question Number 178277 by Sheshdevsahu last updated on 14/Oct/22 $$$$$$if{2}^{pq}-2^{rs}=32;wherep,q,r,s\in \mathbb{Z}$$$$thenpossiblevaluesof$$$$p+q+r+s=??$$$$$$ Terms of Service…

Question Number 112575 by Aina Samuel Temidayo last updated on 08/Sep/20 Answered by Rasheed.Sindhi last updated on 09/Sep/20 $$x^2-3y^2=1376$$$$\because\mathrm{4}\mid\mathrm{1376}\:\:\:\:\:\therefore\:\mathrm{4}\mid{x}^{\mathrm{2}} −\mathrm{3}{y}^{\mathrm{2}} \…

Question Number 112572 by Aina Samuel Temidayo last updated on 08/Sep/20 Commented by mr W last updated on 08/Sep/20 $$seeQ112533$$ Answered by mr…

Question Number 112465 by Aina Samuel Temidayo last updated on 08/Sep/20 Answered by floor(10²Eta[1]) last updated on 08/Sep/20 $$3\mid 3.4^{\mathrm{n}}+51=3(4^{\mathrm{n}}+17)\left(\mathrm{clearly}\mathrm{a}\mathrm{multiple}\mathrm{of}3\right)$$$$\mathrm{9}\mid\mathrm{3}.\mathrm{4}^{\mathrm{n}} +\mathrm{51}\Leftrightarrow\mathrm{3}\mid\mathrm{4}^{\mathrm{n}} +\mathrm{17}\Leftrightarrow\mathrm{3}\mid\left(\mathrm{4}^{\mathrm{n}}…