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 181313 by a.lgnaoui last updated on 23/Nov/22

$$Montrerque$$$$3^{2n+1}+2^{n+2}estdivisiblepar7$$

Answered by mr W last updated on 23/Nov/22

$$3^{2n+1}+2^{n+2}mod7$$$$=3\times {(7+2)}^n+4\times 2^{n}mod7$$$$=3\times 2^n+4\times 2^{n}mod7$$$$=7\times 2^{n}mod7$$$$=0$$

Commented by a.lgnaoui last updated on 24/Nov/22

$$thanks$$

Answered by Acem last updated on 23/Nov/22

$$3^{2n+1}+2^{n+2}=3^{2n}\times 3+2^n\times 2^2$$$$=9^n\times 3+2^n\times 4...\left(1\right)$$$$9^1\equiv 2\left[7\right]\Rightarrow 9^n\equiv 2^n\left[7\right]$$$$3^{2n+1}+2^{n+2}\equiv 2^n\times 3+2^n\times 4=2^n\times 7$$$$\equiv 0\left[7\right]$$$$$$$$Donc{3}^{2n+1}+2^{n+2}estdivisibleparsept$$$$$$

Commented by a.lgnaoui last updated on 24/Nov/22

$$thanks$$

Commented by Acem last updated on 24/Nov/22

$$Derien$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com