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Author: Tinku Tara

1-Show-that-2019-2021-2021-2019-divided-by-2020-2-Show-that-2222-5555-5555-2222-divided-by-7-

Question Number 131507 by Chhing last updated on 05/Feb/21 $$ \\ $$$$\:\:\:\mathrm{1}/\mathrm{Show}\:\mathrm{that}\:\left(\mathrm{2019}\right)^{\mathrm{2021}} +\left(\mathrm{2021}\right)^{\mathrm{2019}} \:\mathrm{divided}\:\:\mathrm{by}\:\mathrm{2020} \\ $$$$\:\:\:\mathrm{2}/\mathrm{Show}\:\mathrm{that}\:\mathrm{2222}^{\mathrm{5555}} +\mathrm{5555}^{\mathrm{2222}} \:\mathrm{divided}\:\:\mathrm{by}\:\mathrm{7} \\ $$$$ \\ $$ Answered by JDamian…

given-x-n-1-1-3-x-n-x-0-2-proof-that-a-0-lt-x-n-2-n-N-b-x-n-is-decreasing-c-lim-n-x-n-

Question Number 431 by 123456 last updated on 25/Jan/15 $$\mathrm{given} \\ $$$${x}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{3}−{x}_{{n}} } \\ $$$${x}_{\mathrm{0}} =\mathrm{2} \\ $$$$\mathrm{proof}\:\mathrm{that} \\ $$$$\mathrm{a}.\mathrm{0}<{x}_{{n}} \leqslant\mathrm{2},{n}\in\mathbb{N} \\ $$$$\mathrm{b}.{x}_{{n}} \:\mathrm{is}\:\mathrm{decreasing}…

please-recommend-problem-and-exercise-book-for-number-theory-where-answers-and-solutions-are-not-given-or-only-given-at-the-end-of-the-book-i-find-it-annoying-when-answers-are-always-right-ne

Question Number 131497 by talminator2856791 last updated on 05/Feb/21 $$\: \\ $$$$\: \\ $$$$\:\mathrm{please}\:\mathrm{recommend}\:\mathrm{problem}\:\mathrm{and}\:\mathrm{exercise}\:\mathrm{book}\:\mathrm{for}\:\mathrm{number}\:\mathrm{theory}\: \\ $$$$\:\mathrm{where}\:\mathrm{answers}\:\mathrm{and}\:\mathrm{solutions}\:\mathrm{are}\:\mathrm{not}\:\mathrm{given}\:\mathrm{or}\:\mathrm{only} \\ $$$$\:\mathrm{given}\:\mathrm{at}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{book}.\:\mathrm{i}\:\mathrm{find}\:\mathrm{it}\:\mathrm{annoying}\:\mathrm{when}\:\mathrm{answers}\:\mathrm{are}\:\mathrm{always}\:\mathrm{right}\:\mathrm{next}\:\mathrm{to}\:\mathrm{the}\:\mathrm{question}. \\ $$$$\:\mathrm{a}\:\mathrm{book}\:\mathrm{that}\:\mathrm{has}\:\mathrm{no}\:\mathrm{solutions}\:\mathrm{would}\:\mathrm{be}\:\mathrm{even}\:\mathrm{greater}. \\ $$$$\:\mathrm{the}\:\mathrm{only}\:\mathrm{such}\:\mathrm{book}\:\mathrm{i}\:\mathrm{have}\:\mathrm{found}\:\mathrm{is}\:\mathrm{250}\:\mathrm{problems}\:\mathrm{in}\:\mathrm{elementary}\:\mathrm{number}\:\mathrm{theory}. \\ $$$$\:\mathrm{thank}. \\…

How-many-digits-are-present-in-periodic-part-for-decimal-expansion-of-1-7-11-

Question Number 427 by 9999 last updated on 25/Jan/15 $$\mathrm{How}\:\mathrm{many}\:\mathrm{digits}\:\mathrm{are}\:\mathrm{present}\:\mathrm{in} \\ $$$$\mathrm{periodic}\:\mathrm{part}\:\mathrm{for}\:\mathrm{decimal}\:\mathrm{expansion} \\ $$$$\mathrm{of}\:\frac{\mathrm{1}}{\mathrm{7}^{\mathrm{11}} }? \\ $$ Commented by 123456 last updated on 02/Jan/15 $$\mathrm{10}^{{n}}…