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For-all-in-0-pi-2-show-that-cos-sin-sin-cos-

Question Number 60849 by Kunal12588 last updated on 26/May/19 $${For}\:{all}\:\theta\:{in}\:\left[\mathrm{0},\:\pi/\mathrm{2}\right]\:{show}\:{that}\:{cos}\left({sin}\theta\right)\geqslant{sin}\left({cos}\theta\right). \\ $$ Commented by Prithwish sen last updated on 26/May/19 $$\mathrm{when}\:\theta\in\left[\mathrm{0},\frac{\pi}{\mathrm{2}}\:\right] \\ $$$$\mathrm{sin}\theta\:\mathrm{and}\:\mathrm{cos}\theta\:\mathrm{lies}\:\mathrm{between}\:\mathrm{0}\:\mathrm{to}\:\mathrm{1} \\ $$$$\therefore\:\mathrm{For}\:\alpha\in\left[\mathrm{0},\mathrm{1}\right]…

Prove-or-disprove-that-there-is-a-positive-integer-suitable-for-n-3-1-n-n-is-divided-by-n-3-1-n-Z-

Question Number 60808 by naka3546 last updated on 26/May/19 $${Prove}\:\:{or}\:\:{disprove}\:\:{that}\:\:{there}\:\:{is} \\ $$$${a}\:\:{positive}\:\:{integer}\:\:{suitable}\:\:{for} \\ $$$$\:\:\:\:\:\:\:{n}^{\mathrm{3}} \:+\:\mathrm{1}\:\:\:\mid\:\:\:{n}!\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\:{n}!\:\:\:{is}\:\:{divided}\:\:{by}\:\:{n}^{\mathrm{3}} \:+\:\mathrm{1}\:\:\right) \\ $$$${n}\:\:\in\:\:\mathbb{Z}^{+} \\ $$ Commented by mr W last…

Question-126318

Question Number 126318 by Algoritm last updated on 19/Dec/20 Commented by mr W last updated on 19/Dec/20 371115746176445351701210713361941528546861949073514542015172437236580034634746971244943788132460150776779198800002366059871900041784732217539059306483834977865973576751345853385981719448969027641920 Answered by MJS_new last updated on 19/Dec/20…