Question and Answers Forum

All Questions      Topic List

Number Theory Questions

Previous in All Question      Next in All Question      

Previous in Number Theory      Next in Number Theory      

Question Number 27922 by Rasheed.Sindhi last updated on 17/Jan/18

$$\mathrm{a},\mathrm{b}\mathrm{\&}\mathrm{c}\mathrm{are}\mathbf{distinct}\mathbf{primes}\mathrm{and}$$$$\mathrm{x},\mathrm{y},\mathrm{z}\in \{0,1,2,...\}.$$$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{number}\mathrm{of}\mathbf{divisors},$$$$\mathbf{common}\mathrm{to}\mathrm{the}\mathbf{numbers}{\mathbf{a}}^{\mathbf{x}}{\mathbf{b}}^{\mathbf{y}}{\mathbf{c}}^{\mathbf{z}},$$$${\mathbf{a}}^{\mathbf{x}}{\mathbf{b}}^{\mathbf{z}}{\mathbf{c}}^{\mathbf{y}},{\mathbf{a}}^{\mathbf{y}}{\mathbf{b}}^{\mathbf{x}}{\mathbf{c}}^{\mathbf{z}},{\mathbf{a}}^{\mathbf{y}}{\mathbf{b}}^{\mathbf{z}}{\mathbf{c}}^{\mathbf{x}},{\mathbf{a}}^{\mathbf{z}}{\mathbf{b}}^{\mathbf{x}}{\mathbf{c}}^{\mathbf{y}}\mathrm{\&}{\mathbf{a}}^{\mathbf{z}}{\mathbf{b}}^{\mathbf{y}}{\mathbf{c}}^{\mathbf{z}}.$$

Commented by mrW2 last updated on 17/Jan/18

$$AccordingtoQ27888,itis{[1+min(x,y,z)]}^3.$$

Commented by Rasheed.Sindhi last updated on 17/Jan/18

$$\mathrm{Yes}\mathrm{sir}\mathrm{I}\mathrm{thought}\mathrm{so}\mathrm{and}\mathrm{can}\mathrm{be}$$$$\mathrm{extended}\mathrm{to}{[1+\min ({\mathrm{x}}_1,{\mathrm{x}}_2,..,{\mathrm{x}}_{\mathrm{n}})]}^{\mathrm{n}}$$$$\mathrm{Common}\mathrm{divisors}:$$$${\mathrm{a}}_1^{0,1,..,\min ({\mathrm{x}}_1,{\mathrm{x}}_2,..,{\mathrm{x}}_{\mathrm{n}})}{\mathrm{a}}_2^{0,1,..,\min ({\mathrm{x}}_1,{\mathrm{x}}_2,..,{\mathrm{x}}_{\mathrm{n}})}...{\mathrm{a}}_{\mathrm{n}}^{0,1,..,\min ({\mathrm{x}}_1,{\mathrm{x}}_2,..,{\mathrm{x}}_{\mathrm{n}})}$$$$\mathrm{Number}\mathrm{of}\mathrm{common}\mathrm{divisors}=$$$${[1+\min ({\mathrm{x}}_1,{\mathrm{x}}_2,..,{\mathrm{x}}_{\mathrm{n}})]}^{\mathrm{n}}$$

Commented by mrW2 last updated on 17/Jan/18

$${That}^{\prime }sabsolutelycorrectsir.$$$$Ithinkyoumeantinlastline$$$${[1+\min ({\mathrm{x}}_1,{\mathrm{x}}_2,..,{\mathrm{x}}_{\mathrm{n}})]}^{\mathrm{n}}$$

Commented by Rasheed.Sindhi last updated on 17/Jan/18

$$\mathrm{Yes}\mathrm{Sir}\mathrm{commit}\mathrm{mistake}\mathrm{mistakenly}.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com