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Sa se determine n intreg , astfel incat 2^n-2^4+1 sa fie patrat perfect.

katos wrote:Sa se determine \( n \) natural astfel incat \( 2^n-15 \) sa fie patrat perfect.

\( 2^n=15+m^2\ \Longrightarrow n\ge 4 \ \ \wedge\ \ m=2p+1\ \Longrightarrow\ 2^n=16+4p(p+1)\ \Longrightarrow

2^{n-4}=1+p(p+1)\ \stackrel {p(p+1)\mathrm{-par}}{\Longrightarrow}\ n=4 \) .

Virgil Nicula wrote:

katos wrote:Sa se determine \( n \) natural astfel incat \( 2^n-15 \) sa fie patrat perfect.

\( 2^n=15+m^2\ \Longrightarrow n\ge 4 \ \ \wedge\ \ m=2p+1\ \Longrightarrow\ 2^n=16+4p(p+1)\ \Longrightarrow

2^{n-4}=1+p(p+1)\ \stackrel {p(p+1)\mathrm{-par}}{\Longrightarrow}\ n=4 \) .

Mersi de raspuns !Dar totusi am doua intrebari de unde m2 si de unde este =m2 cu 2p+1 si ce inseamna par ?

katos wrote: si ce inseamna par ?

enescu wrote:

katos wrote: si ce inseamna par ?

da , dar mai ramane m2 si de unde este =m2 cu 2p+1