Dgdrxrt

How can players take actions together that are impossible otherwise?

Are my PIs rude or am I just being too sensitive?

How do you clear the ApexPages.getMessages() collection in a test?

grandmas drink with lemon juice

Biased dice probability question

Strange behaviour of Check

Did the new image of black hole confirm the general theory of relativity?

Blender game recording at the wrong time

Stars Make Stars

Can a non-EU citizen traveling with me come with me through the EU passport line?

How do I automatically answer y in bash script?

Stopping real property loss from eroding embankment

How does modal jazz use chord progressions?

Slither Like a Snake

Why does this iterative way of solving of equation work?

How can I make names more distinctive without making them longer?

Training a classifier when some of the features are unknown

How to politely respond to generic emails requesting a PhD/job in my lab? Without wasting too much time

Mortgage adviser recommends a longer term than necessary combined with overpayments

3 doors, three guards, one stone

Statistical model of ligand substitution

How many things? AとBがふたつ

Do working physicists consider Newtonian mechanics to be "falsified"?

What is the electric potential inside a point charge?

Using Fermat's Theorem compute .. [duplicate]

-1

$begingroup$

This question already has an answer here:

• 
  Mod of numbers with large exponents
  
  3 answers
  
  

 So here goes the problem :

 Compute:
 2^1234 (mod 11) 
 How would I go about trying to solve this ?

This is what I have tried so far
I know that 2^10 (mod 11) is congruent to 1,but that is about it.

elementary-number-theory

share|cite|improve this question

edited Mar 31 at 19:56

Bill Dubuque

214k29197659

asked Mar 31 at 19:44

TheHedgeTheHedge

43

$endgroup$

marked as duplicate by Bill Dubuque elementary-number-theory
Users with the  elementary-number-theory badge can single-handedly close elementary-number-theory questions as duplicates and reopen them as needed.

StackExchange.ready(function()
if (StackExchange.options.isMobile) return;

$('.dupe-hammer-message-hover:not(.hover-bound)').each(function()
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');

$hover.hover(
function()
$hover.showInfoMessage('',
messageElement: $msg.clone().show(),
transient: false,
position: my: 'bottom left', at: 'top center', offsetTop: -7 ,
dismissable: false,
relativeToBody: true
);
,
function()
StackExchange.helpers.removeMessages();

);
);
);
Mar 31 at 19:56

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

add a comment | 

-1

$begingroup$

This question already has an answer here:

• 
  Mod of numbers with large exponents
  
  3 answers
  
  

 So here goes the problem :

 Compute:
 2^1234 (mod 11) 
 How would I go about trying to solve this ?

This is what I have tried so far
I know that 2^10 (mod 11) is congruent to 1,but that is about it.

elementary-number-theory

share|cite|improve this question

edited Mar 31 at 19:56

Bill Dubuque

214k29197659

asked Mar 31 at 19:44

TheHedgeTheHedge

43

$endgroup$

marked as duplicate by Bill Dubuque elementary-number-theory
Users with the  elementary-number-theory badge can single-handedly close elementary-number-theory questions as duplicates and reopen them as needed.

StackExchange.ready(function()
if (StackExchange.options.isMobile) return;

$('.dupe-hammer-message-hover:not(.hover-bound)').each(function()
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');

$hover.hover(
function()
$hover.showInfoMessage('',
messageElement: $msg.clone().show(),
transient: false,
position: my: 'bottom left', at: 'top center', offsetTop: -7 ,
dismissable: false,
relativeToBody: true
);
,
function()
StackExchange.helpers.removeMessages();

);
);
);
Mar 31 at 19:56

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

add a comment | 

$begingroup$

This question already has an answer here:

• 
  Mod of numbers with large exponents
  
  3 answers
  
  

 So here goes the problem :

 Compute:
 2^1234 (mod 11) 
 How would I go about trying to solve this ?

This is what I have tried so far
I know that 2^10 (mod 11) is congruent to 1,but that is about it.

elementary-number-theory

share|cite|improve this question

edited Mar 31 at 19:56

Bill Dubuque

214k29197659

asked Mar 31 at 19:44

TheHedgeTheHedge

43

$endgroup$

 So here goes the problem :

 Compute:
 2^1234 (mod 11) 
 How would I go about trying to solve this ?

share|cite|improve this question

edited Mar 31 at 19:56

Bill Dubuque

214k29197659

asked Mar 31 at 19:44

TheHedgeTheHedge

43

share|cite|improve this question

edited Mar 31 at 19:56

Bill Dubuque

214k29197659

asked Mar 31 at 19:44

TheHedgeTheHedge

43

edited Mar 31 at 19:56

Bill Dubuque

214k29197659

edited Mar 31 at 19:56

Bill Dubuque

214k29197659

asked Mar 31 at 19:44

TheHedgeTheHedge

43

asked Mar 31 at 19:44

TheHedgeTheHedge

43

2 Answers
2

active

oldest

votes

1

$begingroup$

Hint: You're in the right direction. Write $2^1234 = (2^10)^123cdot2^4$

share|cite|improve this answer

answered Mar 31 at 19:48

lhflhf

168k11172404

$endgroup$

add a comment | 

1

$begingroup$

Hint:

As an immediate consequence of lil' Fermat, for any integer $a$ not divisible by $11$, one has:
$$a^nequiv a^nbmod 10mod 11.$$

share|cite|improve this answer

answered Mar 31 at 19:49

BernardBernard

124k741117

$endgroup$

add a comment | 

1

$begingroup$

Hint: You're in the right direction. Write $2^1234 = (2^10)^123cdot2^4$

share|cite|improve this answer

answered Mar 31 at 19:48

lhflhf

168k11172404

$endgroup$

add a comment | 

1

$begingroup$

Hint: You're in the right direction. Write $2^1234 = (2^10)^123cdot2^4$

share|cite|improve this answer

answered Mar 31 at 19:48

lhflhf

168k11172404

$endgroup$

add a comment | 

$begingroup$

Hint: You're in the right direction. Write $2^1234 = (2^10)^123cdot2^4$

share|cite|improve this answer

answered Mar 31 at 19:48

lhflhf

168k11172404

$endgroup$

share|cite|improve this answer

answered Mar 31 at 19:48

lhflhf

168k11172404

answered Mar 31 at 19:48

lhflhf

168k11172404

answered Mar 31 at 19:48

lhflhf

168k11172404

1

$begingroup$

Hint:

As an immediate consequence of lil' Fermat, for any integer $a$ not divisible by $11$, one has:
$$a^nequiv a^nbmod 10mod 11.$$

share|cite|improve this answer

answered Mar 31 at 19:49

BernardBernard

124k741117

$endgroup$

add a comment | 

1

$begingroup$

Hint:

As an immediate consequence of lil' Fermat, for any integer $a$ not divisible by $11$, one has:
$$a^nequiv a^nbmod 10mod 11.$$

share|cite|improve this answer

answered Mar 31 at 19:49

BernardBernard

124k741117

$endgroup$

add a comment | 

$begingroup$

Hint:

As an immediate consequence of lil' Fermat, for any integer $a$ not divisible by $11$, one has:
$$a^nequiv a^nbmod 10mod 11.$$

share|cite|improve this answer

answered Mar 31 at 19:49

BernardBernard

124k741117

$endgroup$

share|cite|improve this answer

answered Mar 31 at 19:49

BernardBernard

124k741117

answered Mar 31 at 19:49

BernardBernard

124k741117

answered Mar 31 at 19:49

BernardBernard

124k741117