Question Number 85588 by TawaTawa1 last updated on 23/Mar/20
Commented by john santu last updated on 23/Mar/20
$$\mathrm{14},\mathrm{450}\:=\:\frac{{a}\left(\mathrm{4}^{{n}} −\mathrm{1}\right)}{\mathrm{3}} \\ $$$$\mathrm{43},\mathrm{350}\:=\:{a}\:\left(\mathrm{4}^{{n}} −\mathrm{1}\right) \\ $$$${a}\:=\:\frac{\mathrm{43},\mathrm{350}}{\mathrm{4}^{{n}} −\mathrm{1}}\:\Rightarrow\:\mathrm{100}<\frac{\mathrm{43},\mathrm{350}}{\mathrm{4}^{{n}} −\mathrm{1}}<\mathrm{500} \\ $$$$\frac{\mathrm{1}}{\mathrm{500}}\:<\:\frac{\mathrm{4}^{{n}} −\mathrm{1}}{\mathrm{43},\mathrm{350}}<\frac{\mathrm{1}}{\mathrm{100}} \\ $$$$\frac{\mathrm{43},\mathrm{500}}{\mathrm{500}}\:<\:\mathrm{4}^{{n}} −\mathrm{1}<\frac{\mathrm{43},\mathrm{500}}{\mathrm{100}} \\ $$$$ \\ $$
Commented by john santu last updated on 23/Mar/20
$$\mathrm{87}<\mathrm{4}^{{n}} −\mathrm{1}<\mathrm{435} \\ $$$$\mathrm{88}\:<\:\mathrm{4}^{{n}} \:<\:\mathrm{436} \\ $$$$\mathrm{log}_{\mathrm{4}} \left(\mathrm{88}\right)\:<\:{n}\:<\:\mathrm{log}_{\mathrm{4}} \left(\mathrm{436}\right) \\ $$
Commented by TawaTawa1 last updated on 23/Mar/20
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$$$\mathrm{Does}\:\mathrm{the}\:\mathrm{output}\:\mathrm{agree}\:\mathrm{with}\:\mathrm{the}\:\mathrm{formular}? \\ $$
Commented by jagoll last updated on 23/Mar/20
$$\mathrm{3}.\mathrm{229}\:<\:\mathrm{n}\:<\:\mathrm{4}.\mathrm{384} \\ $$$$\mathrm{n}\:=\:\mathrm{4}\:\Rightarrow\:\mathrm{so}\: \\ $$$$\mathrm{a}\:=\:\frac{\mathrm{43},\mathrm{350}}{\mathrm{4}^{\mathrm{4}} −\mathrm{1}}\:=\:\mathrm{170}.\:\mathrm{miss}\:\mathrm{tawa} \\ $$
Commented by jagoll last updated on 23/Mar/20
$$\mathrm{the}\:\mathrm{answer}\:\mathrm{mr}\:\mathrm{john}\:\mathrm{is}\:\mathrm{correct}\:\mathrm{miss}? \\ $$$$\mathrm{i}\:\mathrm{think}\:\mathrm{is}\:\mathrm{correct} \\ $$
Commented by TawaTawa1 last updated on 23/Mar/20
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$