Question

Ma puteti ajuta cu ex. din imagini??
Va rog!

Answer 1

1.
x=252⁹⁰ =(2²×3²×7)⁹⁰
y=1764⁴⁵=(2²×3²×7²)⁴⁵=(2×3×7)⁹⁰
rezulta ca    x>y

2.
A=3²ⁿ⁺²×2⁴ⁿ⁺³+3²ⁿ⁺³×4²⁽ⁿ⁺¹⁾=
=3²ⁿ⁺²×2⁴ⁿ⁺³+3²ⁿ⁺³×2⁴ⁿ⁺⁴=
=3²ⁿ⁺²×2⁴ⁿ⁺³(1+3×2)=
=3²ⁿ⁺²×2⁴ⁿ⁺³×7=
=3²ⁿ×2⁴ⁿ⁺³×3²×7=
=3²ⁿ×2⁴ⁿ⁺³×9×7=
=3²ⁿ×2⁴ⁿ⁺³×63  deci este divizibil cu 63  ⇒ rest=0

n=2015
2n+2=4032
2n+3=4033
4n+3=8063
4n+4=8064

Uc(A)=Uc(3⁴⁰³²×2⁸⁰⁶³+3⁴⁰³³×2⁸⁰⁶⁴)=Uc(1×8+3×6)=Uc(8+18)=Uc(26)=6
Uc(3⁴⁰³²)=Uc(3¹⁰⁰⁸ˣ⁴)=Uc(3⁴)=Uc(81)=1
Uc(2⁸⁰⁶³)=Uc(2²⁰¹⁵ˣ⁴⁺³)=Uc(2³)=8
Uc(3⁴⁰³³)=Uc(3¹⁰⁰⁸ˣ⁴⁺¹)=Uc(3¹)=3
Uc(2⁸⁰⁶⁴)=Uc(2²⁰¹⁶ˣ⁴)=Uc(2⁴)=6
Uc(3⁴⁰³³)=Uc(3¹⁰⁰⁸ˣ⁴⁺¹)=Uc(3¹)=3