aflati numerele

katos · Post by **katos** » Mon Feb 09, 2009 8:26 pm

Aflati numerele naturale x si y pentru care x la put 2 + y la put 2 = 2 la put 101

BurnerD1 · Post by **BurnerD1** » Wed Mar 04, 2009 6:52 pm

adica \( x^2 + y^2 = 2^{101} \)

DrAGos Calinescu · Post by **DrAGos Calinescu** » Wed Mar 04, 2009 7:05 pm

\( x^2,y^2\in {M_4,M_4+1,M_4+2}\Longrightarrow \) x,y numere pare.
Deci \( 4(x_2^2+y_2^2)=2^{101}\Longrightarrow x_2^2+y_2^2=2^{99} \)
Procedam asemanator si deducem ca \( x=2^p, y=2^q \)
Presupunem \( p\ge q \) si impartim prin \( 2^{2q}\Longrightarrow 2^{2(p-q)}+1=2^{101-2q}\Longrightarrow p=q=25\Longrightarrow x=y=2^{50} \)

BurnerD1 · Post by **BurnerD1** » Wed Mar 04, 2009 7:13 pm

\( \mathbb{M}4 \) fiind multiplii lui 4, \( \mathbb{M} 4+1 = {5,9,11, ...} \) ??

DrAGos Calinescu · Post by **DrAGos Calinescu** » Wed Mar 04, 2009 7:15 pm

BurnerD1 · Post by **BurnerD1** » Wed Mar 04, 2009 7:18 pm

Si de unde stii tu asta ? ca \( x^2,y^2 \in M_4, M_{4+1}, M_{4+2} \) ??

DrAGos Calinescu · Post by **DrAGos Calinescu** » Wed Mar 04, 2009 7:21 pm

Sunt formele pe care le poate lua un patrat perfect.

mihai++ · Post by **mihai++** » Thu Mar 05, 2009 8:56 am

burnerd1 te rog frumos sa fi un pic mai politicos ca site ul asta e pt invatat nu pt luat la rost

BurnerD1 · Post by **BurnerD1** » Thu Mar 05, 2009 9:06 am

mihai++ eu nu intreb cu tenta de a jigni sau de "a lua la rost", ci eu intreb pentru a documenta.