Question

If the operation (a mod b) is the remainder of division operation by b, calculate (7^7.777.777 mod 100) + (5^5.555.555 mod 10)?
The answer is 12. Pls tell me step by step how to get its number.

Answer 1

@mathmate @mathmale @skullpatrol @RadEn @princeharryyy

Answer 2

Um, what grade is this? xD

Answer 3

arithmetic for computer science XD

Answer 4

Uhh

Answer 5

yup

Answer 6

what are dots in 7777777

Answer 7

It just takes a little patience!
Make a table, I'll start witht he first 3 entries, and will let you finish it until you find a pattern.
n 7^n mod(7^n,100)
1 7 7
2 49 49
3 343 43
4 ...
If the pattern has a period of k, then 7^7777777\(\equiv\)7^(7777777 mod k), the latter of which can be calculated using a calculator.

You can do the same with 5^5555555 mod 10.

I have verified the answer, which is indeed 12.

Answer 8

I'm sorry. Dots is not decimal symbol.

Answer 9

okay

Answer 10

it can be done manually.

Answer 11

amd yes the answer is right.

Answer 12

it is 12

Answer 13

the pattern will recur every 4x.
Then?

Answer 14

5 to power anything will leave 5 in the end...

see, 5^1 =5
5^2 = 25
5^3 = 125 and so on. and because we have to find the mod we are concerned with last digit of 5^ whatever.

So the remainder of second part would be 5. Right?

Answer 15

I know how to find the remainder. So what?

Answer 16

you are looking for remainder in this question or are you not?

Answer 17

I mean after find the remainder. What we are going to do

Answer 18

So you found k=4,
Next step is to use
7^7777777 mod 100 ≡7^(7777777 mod k) mod 100

Answer 19

we are going to find the remainder for the first one. LOL. We have already done the second part.

Answer 20

when u divide the power 7777777 you would be left with only 1 power every thing else qould be contained in the division by 4.

Answer 21

Owhh... I get it now

Answer 22

@Kevin
You need to find the remainder of the each of 7^7777777 mod 100 and 5^5555555 mod 10. After that, the sum should equal 12.

Answer 23

It would be
7^1 mod 100 + 5^1 mod 100 ?

Answer 24

7^7777777 = 7^1

Answer 25

7^1 mod 100 + 5^1 mod 10 = 7 +5 =12

Answer 26

Sorry, that's what I mean 7^1 mod 100 + 5^1 mod 10

Answer 27

Thx guys

Answer 28

yes it's right.@Kevin

Answer 29

I don't know whom I give the medal since both of you help me. lol