Is $2^{57} + 1$ is a composite number? [closed]
1
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Prove or disprove the following: $2^{57} + 1$ is a composite number.
elementary-number-theory
edited Jan 25 at 5:30
J. W. Tanner
3,0401320
asked Jan 25 at 3:06
Sunita JainSunita Jain
182
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closed as off-topic by The Chaz 2.0, Randall, max_zorn, Math Lover, Kemono Chen Jan 25 at 3:27
This question appears to be off-topic. The users who voted to close gave this specific reason:
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If this question can be reworded to fit the rules in the help center, please edit the question.
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1
$begingroup$
Prove or disprove the following: $2^{57} + 1$ is a composite number.
elementary-number-theory
edited Jan 25 at 5:30
J. W. Tanner
3,0401320
asked Jan 25 at 3:06
Sunita JainSunita Jain
182
$endgroup$
closed as off-topic by The Chaz 2.0, Randall, max_zorn, Math Lover, Kemono Chen Jan 25 at 3:27
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – The Chaz 2.0, Randall, max_zorn, Math Lover, Kemono Chen
If this question can be reworded to fit the rules in the help center, please edit the question.
1
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See here: math.stackexchange.com/help/how-to-ask
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– Randall
Jan 25 at 3:08
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You must be more explanatory, we don't make homeworks
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– El borito
Jan 25 at 3:19
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@Elborito it doesn't matter because people will answer it anyway
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– Randall
Jan 25 at 3:23
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@Randall Yes I know, but she can write the context of the question, it is from of a book or a class or Algebra, etc.
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– El borito
Jan 25 at 3:33
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math.stackexchange.com/questions/641443/…
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– lab bhattacharjee
Jan 25 at 3:52
add a comment |
1
1
1
$begingroup$
Prove or disprove the following: $2^{57} + 1$ is a composite number.
elementary-number-theory
edited Jan 25 at 5:30
J. W. Tanner
3,0401320
asked Jan 25 at 3:06
Sunita JainSunita Jain
182
$endgroup$
Prove or disprove the following: $2^{57} + 1$ is a composite number.
elementary-number-theory
elementary-number-theory
edited Jan 25 at 5:30
J. W. Tanner
3,0401320
asked Jan 25 at 3:06
Sunita JainSunita Jain
182
edited Jan 25 at 5:30
J. W. Tanner
3,0401320
asked Jan 25 at 3:06
Sunita JainSunita Jain
182
edited Jan 25 at 5:30
J. W. Tanner
3,0401320
edited Jan 25 at 5:30
J. W. Tanner
3,0401320
edited Jan 25 at 5:30
J. W. Tanner
3,0401320
3,0401320
asked Jan 25 at 3:06
Sunita JainSunita Jain
182
asked Jan 25 at 3:06
Sunita JainSunita Jain
182
asked Jan 25 at 3:06
Sunita JainSunita Jain
182
182
closed as off-topic by The Chaz 2.0, Randall, max_zorn, Math Lover, Kemono Chen Jan 25 at 3:27
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – The Chaz 2.0, Randall, max_zorn, Math Lover, Kemono Chen
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by The Chaz 2.0, Randall, max_zorn, Math Lover, Kemono Chen Jan 25 at 3:27
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – The Chaz 2.0, Randall, max_zorn, Math Lover, Kemono Chen
If this question can be reworded to fit the rules in the help center, please edit the question.
1
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See here: math.stackexchange.com/help/how-to-ask
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– Randall
Jan 25 at 3:08
$begingroup$
You must be more explanatory, we don't make homeworks
$endgroup$
– El borito
Jan 25 at 3:19
$begingroup$
@Elborito it doesn't matter because people will answer it anyway
$endgroup$
– Randall
Jan 25 at 3:23
$begingroup$
@Randall Yes I know, but she can write the context of the question, it is from of a book or a class or Algebra, etc.
$endgroup$
– El borito
Jan 25 at 3:33
$begingroup$
math.stackexchange.com/questions/641443/…
$endgroup$
– lab bhattacharjee
Jan 25 at 3:52
add a comment |
1
$begingroup$
See here: math.stackexchange.com/help/how-to-ask
$endgroup$
– Randall
Jan 25 at 3:08
$begingroup$
You must be more explanatory, we don't make homeworks
$endgroup$
– El borito
Jan 25 at 3:19
$begingroup$
@Elborito it doesn't matter because people will answer it anyway
$endgroup$
– Randall
Jan 25 at 3:23
$begingroup$
@Randall Yes I know, but she can write the context of the question, it is from of a book or a class or Algebra, etc.
$endgroup$
– El borito
Jan 25 at 3:33
$begingroup$
math.stackexchange.com/questions/641443/…
$endgroup$
– lab bhattacharjee
Jan 25 at 3:52
1
1
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See here: math.stackexchange.com/help/how-to-ask
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– Randall
Jan 25 at 3:08
$begingroup$
See here: math.stackexchange.com/help/how-to-ask
$endgroup$
– Randall
Jan 25 at 3:08
$begingroup$
You must be more explanatory, we don't make homeworks
$endgroup$
– El borito
Jan 25 at 3:19
$begingroup$
You must be more explanatory, we don't make homeworks
$endgroup$
– El borito
Jan 25 at 3:19
$begingroup$
@Elborito it doesn't matter because people will answer it anyway
$endgroup$
– Randall
Jan 25 at 3:23
$begingroup$
@Elborito it doesn't matter because people will answer it anyway
$endgroup$
– Randall
Jan 25 at 3:23
$begingroup$
@Randall Yes I know, but she can write the context of the question, it is from of a book or a class or Algebra, etc.
$endgroup$
– El borito
Jan 25 at 3:33
$begingroup$
@Randall Yes I know, but she can write the context of the question, it is from of a book or a class or Algebra, etc.
$endgroup$
– El borito
Jan 25 at 3:33
$begingroup$
math.stackexchange.com/questions/641443/…
$endgroup$
– lab bhattacharjee
Jan 25 at 3:52
$begingroup$
math.stackexchange.com/questions/641443/…
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– lab bhattacharjee
Jan 25 at 3:52
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2 Answers
2
active
oldest
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3
$begingroup$
We can factor $$2^{57}+1 = left( 2^{19} right)^3+1 = left( left(2^{19} right)^2 -2^{19} + 1 right)left( 2^{19} + 1 right)$$ where both factors are greater than $1$. Therefore, $2^{57}+1$ is composite.
edited Jan 25 at 3:58
Lee David Chung Lin
4,38031242
answered Jan 25 at 3:22
JimmyK4542JimmyK4542
41.2k245107
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add a comment |
5
$begingroup$
Yes: $2^{57}+1equiv(-1)^{57}+1=-1+1=0mod 3$.
answered Jan 25 at 3:15
sranthropsranthrop
7,0941925
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
3
$begingroup$
We can factor $$2^{57}+1 = left( 2^{19} right)^3+1 = left( left(2^{19} right)^2 -2^{19} + 1 right)left( 2^{19} + 1 right)$$ where both factors are greater than $1$. Therefore, $2^{57}+1$ is composite.
edited Jan 25 at 3:58
Lee David Chung Lin
4,38031242
answered Jan 25 at 3:22
JimmyK4542JimmyK4542
41.2k245107
$endgroup$
add a comment |
3
$begingroup$
We can factor $$2^{57}+1 = left( 2^{19} right)^3+1 = left( left(2^{19} right)^2 -2^{19} + 1 right)left( 2^{19} + 1 right)$$ where both factors are greater than $1$. Therefore, $2^{57}+1$ is composite.
edited Jan 25 at 3:58
Lee David Chung Lin
4,38031242
answered Jan 25 at 3:22
JimmyK4542JimmyK4542
41.2k245107
$endgroup$
add a comment |
3
3
3
$begingroup$
We can factor $$2^{57}+1 = left( 2^{19} right)^3+1 = left( left(2^{19} right)^2 -2^{19} + 1 right)left( 2^{19} + 1 right)$$ where both factors are greater than $1$. Therefore, $2^{57}+1$ is composite.
edited Jan 25 at 3:58
Lee David Chung Lin
4,38031242
answered Jan 25 at 3:22
JimmyK4542JimmyK4542
41.2k245107
$endgroup$
We can factor $$2^{57}+1 = left( 2^{19} right)^3+1 = left( left(2^{19} right)^2 -2^{19} + 1 right)left( 2^{19} + 1 right)$$ where both factors are greater than $1$. Therefore, $2^{57}+1$ is composite.
edited Jan 25 at 3:58
Lee David Chung Lin
4,38031242
answered Jan 25 at 3:22
JimmyK4542JimmyK4542
41.2k245107
edited Jan 25 at 3:58
Lee David Chung Lin
4,38031242
edited Jan 25 at 3:58
Lee David Chung Lin
4,38031242
edited Jan 25 at 3:58
Lee David Chung Lin
4,38031242
4,38031242
answered Jan 25 at 3:22
JimmyK4542JimmyK4542
41.2k245107
answered Jan 25 at 3:22
JimmyK4542JimmyK4542
41.2k245107
answered Jan 25 at 3:22
JimmyK4542JimmyK4542
41.2k245107
41.2k245107
add a comment |
add a comment |
5
$begingroup$
Yes: $2^{57}+1equiv(-1)^{57}+1=-1+1=0mod 3$.
answered Jan 25 at 3:15
sranthropsranthrop
7,0941925
$endgroup$
add a comment |
5
$begingroup$
Yes: $2^{57}+1equiv(-1)^{57}+1=-1+1=0mod 3$.
answered Jan 25 at 3:15
sranthropsranthrop
7,0941925
$endgroup$
add a comment |
5
5
5
$begingroup$
Yes: $2^{57}+1equiv(-1)^{57}+1=-1+1=0mod 3$.
answered Jan 25 at 3:15
sranthropsranthrop
7,0941925
$endgroup$
Yes: $2^{57}+1equiv(-1)^{57}+1=-1+1=0mod 3$.
answered Jan 25 at 3:15
sranthropsranthrop
7,0941925
answered Jan 25 at 3:15
sranthropsranthrop
7,0941925
answered Jan 25 at 3:15
sranthropsranthrop
7,0941925
answered Jan 25 at 3:15
sranthropsranthrop
7,0941925
7,0941925
add a comment |
add a comment |
1
$begingroup$
See here: math.stackexchange.com/help/how-to-ask
$endgroup$
– Randall
Jan 25 at 3:08
$begingroup$
You must be more explanatory, we don't make homeworks
$endgroup$
– El borito
Jan 25 at 3:19
$begingroup$
@Elborito it doesn't matter because people will answer it anyway
$endgroup$
– Randall
Jan 25 at 3:23
$begingroup$
@Randall Yes I know, but she can write the context of the question, it is from of a book or a class or Algebra, etc.
$endgroup$
– El borito
Jan 25 at 3:33
$begingroup$
math.stackexchange.com/questions/641443/…
$endgroup$
– lab bhattacharjee
Jan 25 at 3:52