Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 176279 by CrispyXYZ last updated on 15/Sep/22

Proof that : ∄n∈Z, n^2 +1≡0(mod 4)

Proofthat:∄n∈Z,n2+1≡0(mod4)

Answered by mahdipoor last updated on 15/Sep/22

I> n=2k+1 ⇒n^2 +1=4(k^2 +k)+2≡^4 2 II> n=2k ⇒n^2 +1=4k^2 +1≡^4 1 I & II ⇒ ∄n∈Z , n^2 +1≡^4 0

I>n=2k+1⇒n2+1=4(k2+k)+2≡42II>n=2k⇒n2+1=4k2+1≡41I&II⇒∄n∈Z,n2+1≡40

Terms of Service

Privacy Policy

Contact: info@tinkutara.com