Question

What is 6^1001 mod 7 @ganeshie8 @Luigi0210 @wio @e.mccormick @shamil98 @dan815 @wolfe8 @nincompoop @Ashleyisakitty @Isaiah.Feynman @kewlgeek555 @tester97 @Mashy @adrynicoleb @sourwing @dpasingh @RaphaelFilgueiras

Answer 1

\(\large 6^{1001} \equiv (-1)^{1001} \mod 7\)

Answer 2

maybe you can use a ti-84 calculator? anyways im not sure because idk how to solve that

Answer 3

did u watch amelie movie @tester97

Answer 4

Lol everyone has been asking me that but no its just a screenshot from a clip of the movie.

Answer 5

its a very good movi... :)

Answer 6

I will check it out ^_^

Answer 7

il pm u the link on viooz

Answer 8

ok :)

Answer 9

@TanteAnna it simplifies to -1..

Answer 10

what is this -1^1001 why is it equivalent to that

Answer 11

\(6 \equiv -1 \mod 7\)

Answer 12

above expression means :

6 leaves a remainder -1, when divided by 7

Answer 13

oh ok

Answer 14

another easy way to think it is :

(6- (-1)) is divisible by 7

Answer 15

i was thinking
6 mod 7 = 6
36 mod 7 = 1
36*6 mod 7 = 6
36*36 mod 7 = 1
and so on
so even exponent is 1 and odd exponent = 6?

Answer 16

that works !

Answer 17

leaving a remainder 6 is same as leaving a remainder -1

Answer 18

remainder = 6 : overflow is 6
remainder = -1 : lacking 1

both are same when talking about remainders

Answer 19

true

Answer 20

here, -1 makes the life simple as we have a big power

Answer 21

why does it work!

Answer 22

what is 7^100 mod 8?

Answer 23

7?

Answer 24

it works cuz of below theorem : (can be proven easily)

if \(a\) leaves a remainder \(r\) when divided by \(b\), then :
\(a^n\) leaves a remainder \(r^n\) when divided by \(b\)

Answer 25

yup !

Answer 26

wai no even so 1?

Answer 27

oh yes, (-1)^100 = 1

Answer 28

interesting

Answer 29

so remainder is 1, not 7

Answer 30

what is 5^100 mod 7
2??

Answer 31

nope

Answer 32

4?

Answer 33

no no it is 2 WOW O_O how

Answer 34

math is mysterious

Answer 35

5^100 mod 7 = 2^100 mod 7 = 2^(3*33+1) mod 7 = 2*8^33 mod 7 = 2

Answer 36

56^100 mod 23

Answer 37

56^100 mod 23

10^100 mod 23

Answer 38

wat u wana do next uhmm

Answer 39

23-56

Answer 40

56^100 mod 23

10^100 mod 23

100^50 mod 23

8^50 mod 23

Answer 41

keep reducing it..

Answer 42

k start from beginning teach me from start

Answer 43

xD
this example ? or congruences ?

Answer 44

congruences

Answer 45

5 small things we need to cover, to be able to play wid remainders at will