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a-b-c-d-N-a-b-c-d-is-quadruple-of-a-b-c-d-such-that-b-a-2-1-c-b-2-1-d-c-2-1-a-b-c-d-is-odd-number-s-k-is-

Question Number 84206 by naka3546 last updated on 10/Mar/20 $${a},\:{b},\:{c},\:{d}\:\:\in\:\:\mathbb{N} \\ $$$$\left({a},\:{b},\:{c},\:{d}\right)\:\:{is}\:\:{quadruple}\:\:{of}\:\:{a},\:{b},\:{c},\:{d}\:\:{such}\:\:{that} \\ $$$$\:\:\:\:\:\:\:\:{b}\:\:=\:\:{a}^{\mathrm{2}} \:+\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:{c}\:\:=\:\:{b}^{\mathrm{2}} \:+\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:{d}\:\:=\:\:{c}^{\mathrm{2}} \:+\:\mathrm{1} \\ $$$$\tau\left({a}\right)\:+\:\tau\left({b}\right)\:+\:\tau\left({c}\right)\:+\:\tau\left({d}\right)\:\:{is}\:\:\:{odd}\:\:{number}\left({s}\right)\:. \\ $$$$\tau\left({k}\right)\:\:{is}\:\:{the}\:\:{number}\:\:{of}\:\:{positive}\:\:{divisor}\:\:{of}\:\:\:{natural}\:\:{number}\:\:{k}\:.…

Question-84152

Question Number 84152 by naka3546 last updated on 09/Mar/20 Commented by MJS last updated on 09/Mar/20 $$\mathrm{we}\:\mathrm{have}\:\mathrm{to}\:\mathrm{find}\:\mathrm{for}\:\mathrm{which}\:\mathrm{values}\:\mathrm{of}\:{n}\:\mathrm{there} \\ $$$$\mathrm{is}\:\mathrm{such}\:\mathrm{an}\:{x}\:\mathrm{at}\:\mathrm{all}… \\ $$$$\mathrm{it}\:\mathrm{works}\:\mathrm{for}\:{n}=\mathrm{3}\:\mathrm{but}\:\mathrm{not}\:\mathrm{for}\:{n}=\mathrm{2}\:\mathrm{and}\:{n}=\mathrm{4} \\ $$$$… \\ $$…