Menu Close

Category: Number Theory

Please-any-note-on-how-to-find-the-first-digit-first-two-digit-and-first-three-digits-of-any-power-

Question Number 46576 by Tawa1 last updated on 28/Oct/18 $$\mathrm{Please}\:\mathrm{any}\:\mathrm{note}\:\mathrm{on}\:\mathrm{how}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{digit},\:\mathrm{first}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{and}\:\mathrm{first}\:\mathrm{three}\:\mathrm{digits} \\ $$$$\mathrm{of}\:\mathrm{any}\:\mathrm{power} \\ $$ Commented by hassentimol last updated on 30/Oct/18 $$ \\ $$$$\mathrm{I}'\mathrm{m}\:\mathrm{not}\:\mathrm{sure}\:\mathrm{at}\:\mathrm{all}\:\mathrm{but}\:\mathrm{I}\:\mathrm{think}\:\mathrm{that},\:\mathrm{according} \\…

Find-n-N-n-100-4-2-n-n-3-Note-that-S-denotes-the-cardinality-or-number-of-elements-of-a-set-S-

Question Number 112011 by Aina Samuel Temidayo last updated on 05/Sep/20 $$\mathrm{Find}\:\mid\left\{\mathrm{n}\in\mathbb{N}\mid\mathrm{n}\leqslant\mathrm{100},\:\mathrm{4}!\mid\mathrm{2}^{\mathrm{n}} −\mathrm{n}^{\mathrm{3}} \right\}\mid. \\ $$$$\left(\mathrm{Note}\:\mathrm{that}\:\mid\mathrm{S}\mid\:\mathrm{denotes}\:\mathrm{the}\:\mathrm{cardinality}\right. \\ $$$$\left.\mathrm{or}\:\mathrm{number}\:\mathrm{of}\:\mathrm{elements}\:\mathrm{of}\:\mathrm{a}\:\mathrm{set},\mathrm{S}\right). \\ $$ Answered by Rasheed.Sindhi last updated…

Suppose-x-y-z-N-yz-x-is-prime-yz-x-zx-y-yz-x-xy-z-Find-all-possible-values-of-xy-z-zx-y-yz-x-2-

Question Number 112004 by Aina Samuel Temidayo last updated on 05/Sep/20 $$\mathrm{Suppose}\:\mathrm{x},\mathrm{y},\mathrm{z}\:\in\mathbb{N},\:\left(\mathrm{yz}+\mathrm{x}\right)\:\mathrm{is}\:\mathrm{prime} \\ $$$$\left(\mathrm{yz}+\mathrm{x}\right)\mid\left(\mathrm{zx}+\mathrm{y}\right),\:\left(\mathrm{yz}+\mathrm{x}\right)\mid\left(\mathrm{xy}+\mathrm{z}\right). \\ $$$$\mathrm{Find}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\: \\ $$$$\frac{\left(\mathrm{xy}+\mathrm{z}\right)\left(\mathrm{zx}+\mathrm{y}\right)}{\left(\mathrm{yz}+\mathrm{x}\right)^{\mathrm{2}} }. \\ $$ Terms of Service Privacy…

1-5-1-3-7-1-3-5-9-1-3-5-7-95-99-

Question Number 111973 by bobhans last updated on 05/Sep/20 $$\frac{\mathrm{1}}{\mathrm{5}!!}\:+\:\frac{\mathrm{1}.\mathrm{3}}{\mathrm{7}!!}\:+\:\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{9}!!}\:+\:…\:+\:\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}.\mathrm{7}….\mathrm{95}}{\mathrm{99}!!}\:=? \\ $$ Commented by Dwaipayan Shikari last updated on 05/Sep/20 $$\mathrm{1}.\mathrm{3}.\mathrm{5}.\mathrm{7}.\mathrm{9}.\mathrm{11}…{n}=\frac{\left(\mathrm{2}{n}\right)!}{\mathrm{2}.\mathrm{4}.\mathrm{6}.\mathrm{8}.\mathrm{10}..{n}}=\frac{\left(\mathrm{2}{n}\right)!}{\mathrm{2}^{{n}} .{n}!} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\mathrm{48}}…

Let-N-be-the-greatest-multiple-of-36-all-of-whose-digits-are-even-and-no-two-of-whose-digits-are-the-same-Find-the-remainder-when-N-is-divided-by-1000-

Question Number 111831 by Aina Samuel Temidayo last updated on 05/Sep/20 $$\mathrm{Let}\:\mathrm{N}\:\mathrm{be}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{36}\:\mathrm{all} \\ $$$$\mathrm{of}\:\mathrm{whose}\:\mathrm{digits}\:\mathrm{are}\:\mathrm{even}\:\mathrm{and}\:\mathrm{no}\:\mathrm{two}\:\mathrm{of} \\ $$$$\mathrm{whose}\:\mathrm{digits}\:\mathrm{are}\:\mathrm{the}\:\mathrm{same}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{remainder}\:\mathrm{when}\:\mathrm{N}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{1000}. \\ $$ Answered by Rasheed.Sindhi last updated…

How-many-triples-of-positive-integers-x-y-z-satisfy-79x-80y-81z-2016-

Question Number 111730 by Aina Samuel Temidayo last updated on 04/Sep/20 $$\mathrm{How}\:\mathrm{many}\:\mathrm{triples}\:\mathrm{of}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\:\mathrm{satisfy}\: \\ $$$$\mathrm{79x}+\mathrm{80y}+\mathrm{81z}\:=\mathrm{2016} \\ $$ Commented by kaivan.ahmadi last updated on 05/Sep/20…

Assuming-FLT-prove-Fermat-Euler-theorem-a-n-1-n-2-a-n-1-mod-n-

Question Number 111704 by Aina Samuel Temidayo last updated on 04/Sep/20 $$\mathrm{Assuming}\:\mathrm{FLT},\:\mathrm{prove}\:\mathrm{Fermat}−\mathrm{Euler} \\ $$$$\mathrm{theorem}:\:\left(\mathrm{a},\mathrm{n}\right)\:=\mathrm{1},\mathrm{n}\geqslant\mathrm{2}\Rightarrow\mathrm{a}^{\emptyset\left(\mathrm{n}\right)} \equiv\mathrm{1}\left(\mathrm{mod}\right. \\ $$$$\left.\mathrm{n}\right) \\ $$ Answered by Aina Samuel Temidayo last…

Please-help-Find-all-the-general-solution-of-6x-8y-5z-101-I-got-x-48-45m-4n-y-48-45m-3n-z-1-2m-Please-

Question Number 46157 by Tawa1 last updated on 21/Oct/18 $$\mathrm{Please}\:\mathrm{help}. \\ $$$$\:\:\:\:\:\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\:\:\:\:\:\:\:\mathrm{6x}\:+\:\mathrm{8y}\:+\:\mathrm{5z}\:=\:\mathrm{101}\:. \\ $$$$ \\ $$$$\mathrm{I}\:\mathrm{got}:\:\:\:\:\:\:\:\:\mathrm{x}\:=\:−\:\mathrm{48}\:+\:\mathrm{45m}\:+\:\mathrm{4n} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\:=\:\:\:\:\:\mathrm{48}\:+\:\mathrm{45m}\:−\:\mathrm{3n} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{z}\:=\:\:\:\:\:\:\:\mathrm{1}\:−\:\mathrm{2m} \\ $$$$ \\ $$$$\mathrm{Please}\:\mathrm{help}.\:\:\mathrm{Am}\:\mathrm{confused}.\: \\…