1.Determinati nr prime abc barat stiind ca 34 supra a la puterea 2+b la puterea 3 +c la puterea 4 apartin N
2.Scrieti nemarul 51 la puterea 2009 ca o diferenta de 2 patrate perfecte.
3.Cate cifre de 1 are numarul N=1+91+991+……..99……91(intre 99…….91 sunt 2009 cf)
4.Fie a=2 la puterea n+5*3 la n+1+2 la n+2*3 la n
b=2 la 2n+3 * 3 la n+1 + 4 la n+1*3n+2
a)calculati 5b:a
b)sa se determine n apartina lui N stiind ca 5b=12a
5.Aflati numerele de forma abc barat,stiind ca fractia a*(a0c barat -b0c barat) supra b*(21b barat-63c barat) este ireductibila si nenula
51^2009=51×51^2008=(100-49)x51^2008=100×51^2008-49×51^2008=
10^2x(51^1004)^2-7^2x(51^1004)^2=(10×51^1004)^2-(7×51^1004)^2
abc barat=? a.i 34/a^2+b^3+c^4 nr natural
fractia este nr natural daca numitorul imparte exact numaratorul.Notam D34
={1,2,17,34}
a^2+b^3+c^4=1, anenul prin incercaria^2=1,b^3=0 c^4=0=>a+1, b+0, c=0 abc barat=100.
numitorul=2 a^2=1,b^3=1 c^4=0, a=1, b=1 c=0 abc barat =110 sau a^2=1
b^3=0,c^4=1 =>a=1 b=0 c=1 abc barat=101
numitorul=17 a^2=16 b^3=1 C^4=0=> a=4, b=1 c=0 abcbarat=410 sau
a^2=16, b^3=0 c^4=1=> a=4, b=0, c=1 abcbarat=401 saua^2=9b^3=8
c=0=>a=3, b=2 c=0 abc=320 saua^2=9,b^3=0 c^4=1 a=3,b=0 c=1, abc=
301 saua^2=1 b^3=0 c^4=16 =>a=1 b=0 c=2 abc bar.=102
numitorul=34 a^2=25 b^3=8 c^4=1 A=5, b=2 c=1 abc bar.=521 etc
anulat