Question Number 28186 by Tinkutara last updated on 25/Jan/18 $${Find}\:{the}\:{number}\:{of}\:{positive}\:{integers} \\ $$$${x}\:{such}\:{that}\:\left[\frac{{x}}{{m}−\mathrm{1}}\right]=\left[\frac{{x}}{{m}+\mathrm{1}}\right],\:{for}\:{a} \\ $$$${particular}\:{integer}\:{m}\geqslant\mathrm{2}. \\ $$$$\left[\:\right]\:{means}\:{G}.{I}.{F}. \\ $$ Commented by abdo imad last updated on…
Question Number 27936 by Tinkutara last updated on 17/Jan/18 Commented by Rasheed.Sindhi last updated on 19/Jan/18 $$\mathrm{p}^{\mathrm{2}} +\mathrm{7pq}+\mathrm{q}^{\mathrm{2}} =\mathrm{n}^{\mathrm{2}} \:\:;\:\mathrm{n}\in\mathbb{Z} \\ $$$$\mathrm{p}^{\mathrm{2}} +\mathrm{7pq}+\mathrm{q}^{\mathrm{2}} −\mathrm{n}^{\mathrm{2}} =\mathrm{0}…
Question Number 27922 by Rasheed.Sindhi last updated on 17/Jan/18 $$\mathrm{a},\mathrm{b}\:\&\:\mathrm{c}\:\mathrm{are}\:\boldsymbol{\mathrm{distinct}}\:\boldsymbol{\mathrm{primes}}\:\mathrm{and} \\ $$$$\mathrm{x},\mathrm{y},\mathrm{z}\in\left\{\mathrm{0},\mathrm{1},\mathrm{2},…\right\}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\boldsymbol{\mathrm{divisors}}, \\ $$$$\boldsymbol{\mathrm{common}}\:\mathrm{to}\:\mathrm{the}\:\boldsymbol{\mathrm{numbers}}\:\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{y}}} \boldsymbol{\mathrm{c}}^{\boldsymbol{\mathrm{z}}} , \\ $$$$\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{z}}} \boldsymbol{\mathrm{c}}^{\boldsymbol{\mathrm{y}}} ,\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{y}}} \boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{x}}}…
Question Number 27888 by Rasheed.Sindhi last updated on 16/Jan/18 $$\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{are}\:\boldsymbol{\mathrm{distinct}}\:\boldsymbol{\mathrm{primes}}\:\mathrm{and} \\ $$$$\mathrm{x},\mathrm{y}\in\left\{\mathrm{0},\mathrm{1},\mathrm{2},…\right\}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{divisors}} \\ $$$$\boldsymbol{\mathrm{common}}\:\mathrm{to}\:\mathrm{the}\:\boldsymbol{\mathrm{numbers}}\:\left(\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{y}}} \right) \\ $$$$\boldsymbol{\mathrm{and}}\:\left(\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{y}}} \boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{x}}} \right)? \\ $$ Commented…
Question Number 158914 by amin96 last updated on 10/Nov/21 $$\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}\boldsymbol{\mathrm{n}}+\mathrm{1}\right)^{\mathrm{3}} }=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 27816 by Rasheed.Sindhi last updated on 15/Jan/18 $$\mathrm{If}\:\mathrm{N}\:\mathrm{is}\:\boldsymbol{\mathrm{perfect}}\:\boldsymbol{\mathrm{nth}}\:\boldsymbol{\mathrm{power}},\:\mathrm{prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\mathrm{n}\:\mid\:\left(\mathrm{d}\left(\mathrm{N}\right)−\mathrm{1}\right)\: \\ $$$$\left[{Where}\:\mathrm{d}\left(\mathrm{N}\right)\:{denotes}\:\boldsymbol{{number}}\right. \\ $$$$\left.\boldsymbol{{of}}\:\boldsymbol{{divisors}}\:\boldsymbol{{of}}\:\mathrm{N}\right] \\ $$$$\mathrm{Also}\:\mathrm{show}\:\mathrm{by}\:\mathrm{an}\:\mathrm{example}\:\mathrm{that}\:\mathrm{its} \\ $$$$\mathrm{vice}\:\mathrm{versa}\:\mathrm{is}\:\mathrm{not}\:\mathrm{necessarily}\:\mathrm{correct}. \\ $$ Commented by Rasheed.Sindhi…
If-the-number-of-divisors-of-a-number-is-odd-prove-that-the-number-is-perfect-square-and-vice-versa-
Question Number 27767 by Rasheed.Sindhi last updated on 14/Jan/18 $$\mathrm{If}\:\mathrm{the}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{divisors}}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{number}\:\mathrm{is}\:\boldsymbol{\mathrm{odd}},\mathrm{prove}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{is}\:\boldsymbol{\mathrm{perfect}}\:\boldsymbol{\mathrm{square}}\:\mathrm{and} \\ $$$$\mathrm{vice}\:\mathrm{versa}. \\ $$ Answered by mrW2 last updated on 14/Jan/18…
Question Number 93241 by Ayod 19 last updated on 12/May/20 $$\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}+\mathrm{1}} =\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2019}}\right)^{\mathrm{2019}} \\ $$$$\mathrm{Find}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:{x} \\ $$ Answered by prakash jain last updated on 12/May/20 $${x}=−\mathrm{2020}…
Question Number 93209 by Rasheed.Sindhi last updated on 11/May/20 Commented by Rasheed.Sindhi last updated on 12/May/20 $$\mathcal{X}{cellent}\:{Aproach}\:{Sir}! \\ $$ Commented by Rasheed.Sindhi last updated on…
Question Number 27404 by sirigidiravikumar@gmail.com last updated on 06/Jan/18 $$\left(\mathrm{1}\right).{the}\:{mean}\:{of}\:\mathrm{14}.\mathrm{9}.\mathrm{22}.\mathrm{14}.\mathrm{22}.\mathrm{18} \\ $$ Answered by Rasheed.Sindhi last updated on 06/Jan/18 $$\frac{\mathrm{9}+\mathrm{14}×\mathrm{2}+\mathrm{18}+\mathrm{22}×\mathrm{2}}{\mathrm{6}}=\frac{\mathrm{33}}{\mathrm{2}} \\ $$ Terms of Service…