Question

Determinati ultima cifra a numerelor:
a) 7 la puterea 395
b)2 la puterea 54+3 la puterea 99
(dau coroana) ​

Answer 1

a) u(7^395)

7^1=7

7^2=49

7^3=343

7^4=.....1

7^5=....7

...............

395:4=98 rest 3

=> u(7^395)=u(7^3)=3

b) u(2^54+3^99)

u(2^54)

2^1=2

2^2=4

2^3=8

2^4=16

2^5=32

.................

54:4=13 rest 2

=> u(2^54)=u(2^2)=4

u(3^99)

3^1=3

3^2=9

3^3=27

3^4=81

3^5=...3

.................

99:4=24 rest 3

=> u(3^99)=u(3^3)=7

u(2^54+3^99)=u(4+7)=u(11)=1

Succes!

Answer 2

Răspuns:

Explicație pas cu pas:

a) 7^395

7^1=7      rang 4k+1

7²=49      rang 4k+2

7³=343     rang 4k+3

7^4=2401   rang 4k+4

7^5=16807

puterea 395:4=98   rest 3   u(7^395)=3

b)2^54+3^99

2^1=2

2²=4

2³=8

2^4=16

2^5=32

Puterea 54 :4=13 rest  2  ⇒u(2^54)=4

3^1=3      rang 3k+1

3²=9       rang 3k+2

3³=81      rang 3k+3

3^4=243

3^5=729

puterea 99:3=33    ⇒u(3^99)=1

u(2^54+3^99)=u(2^54)+u(3^99)=4+1=5