goformit100
  • goformit100
Find the remainder when 2^1990 is divided by 1990.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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goformit100
  • goformit100
@mayankdevnani
ParthKohli
  • ParthKohli
Mod arithmetic :') @terenzreignz
terenzreignz
  • terenzreignz
Why me? :/

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More answers

ParthKohli
  • ParthKohli
Because you.
goformit100
  • goformit100
In this question How to square to so much power ?
terenzreignz
  • terenzreignz
Might have to resort to totients..... @ParthKohli ?
goformit100
  • goformit100
Sir if i use the exponent rule will it work here ?
ParthKohli
  • ParthKohli
Ah! Euler's Theorem!
anonymous
  • anonymous
factor 1990 first
terenzreignz
  • terenzreignz
Time to doodle... \[\large 2^{1990}=4^{995}\]
goformit100
  • goformit100
How to factor it ?
anonymous
  • anonymous
how to factor 1990?
terenzreignz
  • terenzreignz
What is 4^5? \[\Large = 1024^{199}\]
goformit100
  • goformit100
Yes @satellite73
anonymous
  • anonymous
try \(2\times 5\times 199\)
mayankdevnani
  • mayankdevnani
1990 = 10*199 = 2* 5* 199
terenzreignz
  • terenzreignz
\[\large 1024^{199}=1024\cdot 1024^{198}=1024\cdot 2048^{99}\]
goformit100
  • goformit100
try \(2\times 5\times 199\) means ?
terenzreignz
  • terenzreignz
Now let's start working some "mod magic" and reduce the bases at mod 1990 \[\Large =_{(mod \ 1990)} \ \ 1024\cdot 58^{99}\]
mayankdevnani
  • mayankdevnani
|dw:1367281405845:dw|
mayankdevnani
  • mayankdevnani
ok @goformit100
goformit100
  • goformit100
ok So LCM can be take as a good way of factorizing numbers ok ?
terenzreignz
  • terenzreignz
\[\Large \equiv 1024\cdot 58 \cdot 58^{98}\]
mayankdevnani
  • mayankdevnani
yaaa @goformit100
mayankdevnani
  • mayankdevnani
it is the best way!!!
terenzreignz
  • terenzreignz
\[\Large \equiv 1682 \cdot 1374^{49}\] gah... possibly inefficient...
goformit100
  • goformit100
ok
terenzreignz
  • terenzreignz
\[\Large\equiv 678\cdot (-616)^{48}\]
terenzreignz
  • terenzreignz
This is daunting.
anonymous
  • anonymous
\(1990=2\times 5\times 199\) and \(2^2\equiv 4(5) \) also \(2^{198}\equiv 1(199)\) by fermat
goformit100
  • goformit100
Mods Sir(s) I have to make you know that the Equation you are posting have not opened yet
anonymous
  • anonymous
actually this is kind of a pain isn't it
amistre64
  • amistre64
if you are seeing "math processing error", try refreshing
goformit100
  • goformit100
What to do ?
terenzreignz
  • terenzreignz
\[\Large \equiv 678\cdot (1356)^{24}\]
goformit100
  • goformit100
Yo It's done...Mods you'll great REFRESHING WORKED. No SEE
goformit100
  • goformit100
Now I can see
terenzreignz
  • terenzreignz
\[\Large \equiv 678 \cdot (-634)^{24}\equiv678\cdot (634)^{24}\]
goformit100
  • goformit100
2^1990 is divided by 1990 what to actually for this ?
amistre64
  • amistre64
2^1990 2^11 = 2048 = 38 mod 1990 2^(11(180)+10) is what i had in mond :)
terenzreignz
  • terenzreignz
I lack creativity, guys :)
goformit100
  • goformit100
@mikaela19900630 you may too se the question I have posted now.
goformit100
  • goformit100
Thank you all of you. I can do these type of question Now :)
goformit100
  • goformit100
*from Now
terenzreignz
  • terenzreignz
\[\Large \equiv 678\cdot (-24)^{24}\equiv 678\cdot 24^{24}\]
terenzreignz
  • terenzreignz
cr*p... sorry \[\Large \equiv 678\cdot (-24)^{\color{red}{12}}\equiv 678\cdot 24^{\color{red}{12}}\]
goformit100
  • goformit100
Thank You Very Much.

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