Răspuns :
4.
a) 2^83-(2²)^41=2^83-2^82=2^82(2-1)=2^82=(2^41)²-p.p
b) 11*(5^21-5^20-5^18)=11*5^18(5^3-5^2-1)=11*5^18*99=11*3²*11*(5^9)²=11²*3²*(5^9)²-p.p
3
a) 2^35;(2²)^18; (2³)^11
2^33; 2^35; 2^36
b)
3^61;( 3²)^29;( 3³)^20
3^58; 3^60; 3^61
c)
(5³)^14; (5²)^20; 5^39
5^39; 5^40; 5^42
a) 2^83-(2²)^41=2^83-2^82=2^82(2-1)=2^82=(2^41)²-p.p
b) 11*(5^21-5^20-5^18)=11*5^18(5^3-5^2-1)=11*5^18*99=11*3²*11*(5^9)²=11²*3²*(5^9)²-p.p
3
a) 2^35;(2²)^18; (2³)^11
2^33; 2^35; 2^36
b)
3^61;( 3²)^29;( 3³)^20
3^58; 3^60; 3^61
c)
(5³)^14; (5²)^20; 5^39
5^39; 5^40; 5^42
[tex]3^{2n-3} = 27 ^{7} : 9^{2}
\\ 3^{2n-3}= 3 ^{63} : 3^{4}
\\ 3^{2n-3}= 3^{59}[/tex]
2n-3=59
2n= 62
n= 62 : 2
n= 31.
1b) [tex]5^{3n + 1} = 25^{11} \\ 5^{3n+1}=5^{22}[/tex]
3n+ 1= 22
3n=21
n= 7
[tex]7^{n+1} : 7 ^4 = 49 ^8 \\ 7^{n+1-4}= 7^(2 x 8) \\ 7^{n-3}= 7^{16}[/tex]
n-3=16
n=19
2a)[tex]2^{33} cu 3^{22} \\ 2^{11^3} cu 3^{11^2} \\ 6^{11}=6^{11}[/tex]
2n-3=59
2n= 62
n= 62 : 2
n= 31.
1b) [tex]5^{3n + 1} = 25^{11} \\ 5^{3n+1}=5^{22}[/tex]
3n+ 1= 22
3n=21
n= 7
[tex]7^{n+1} : 7 ^4 = 49 ^8 \\ 7^{n+1-4}= 7^(2 x 8) \\ 7^{n-3}= 7^{16}[/tex]
n-3=16
n=19
2a)[tex]2^{33} cu 3^{22} \\ 2^{11^3} cu 3^{11^2} \\ 6^{11}=6^{11}[/tex]