the number $sqrt{1+5^n+6^n+11^n}$ is an integer [closed]
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How can i prove that $sqrt{1+5^n+6^n+11^n}$ is an integer??
PS : i shouldn't use induction
algebra-precalculus elementary-number-theory arithmetic
edited Nov 28 at 22:32
amWhy
191k28224439
asked Nov 28 at 22:15
FADZA
274
closed as off-topic by amWhy, KReiser, Cesareo, Strants, Lord Shark the Unknown Nov 29 at 5:44
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, KReiser, Cesareo, Strants
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
1
down vote
favorite
How can i prove that $sqrt{1+5^n+6^n+11^n}$ is an integer??
PS : i shouldn't use induction
algebra-precalculus elementary-number-theory arithmetic
edited Nov 28 at 22:32
amWhy
191k28224439
asked Nov 28 at 22:15
FADZA
274
closed as off-topic by amWhy, KReiser, Cesareo, Strants, Lord Shark the Unknown Nov 29 at 5:44
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, KReiser, Cesareo, Strants
If this question can be reworded to fit the rules in the help center, please edit the question.
3
It doesn't work for $n=1$. Sorry, it doesn't work for all $n in mathbb N$. As of now, $sqrt{23} notin mathbb Z$.
– amWhy
Nov 28 at 22:17
Does it even hold for $n=1$?
– Quang Hoang
Nov 28 at 22:17
sorry i have to remake my question !!
– FADZA
Nov 28 at 22:20
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
How can i prove that $sqrt{1+5^n+6^n+11^n}$ is an integer??
PS : i shouldn't use induction
algebra-precalculus elementary-number-theory arithmetic
edited Nov 28 at 22:32
amWhy
191k28224439
asked Nov 28 at 22:15
FADZA
274
How can i prove that $sqrt{1+5^n+6^n+11^n}$ is an integer??
PS : i shouldn't use induction
algebra-precalculus elementary-number-theory arithmetic
algebra-precalculus elementary-number-theory arithmetic
edited Nov 28 at 22:32
amWhy
191k28224439
asked Nov 28 at 22:15
FADZA
274
edited Nov 28 at 22:32
amWhy
191k28224439
asked Nov 28 at 22:15
FADZA
274
edited Nov 28 at 22:32
amWhy
191k28224439
edited Nov 28 at 22:32
amWhy
191k28224439
edited Nov 28 at 22:32
amWhy
191k28224439
191k28224439
asked Nov 28 at 22:15
FADZA
274
asked Nov 28 at 22:15
FADZA
274
asked Nov 28 at 22:15
FADZA
274
274
closed as off-topic by amWhy, KReiser, Cesareo, Strants, Lord Shark the Unknown Nov 29 at 5:44
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, KReiser, Cesareo, Strants
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by amWhy, KReiser, Cesareo, Strants, Lord Shark the Unknown Nov 29 at 5:44
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, KReiser, Cesareo, Strants
If this question can be reworded to fit the rules in the help center, please edit the question.
3
It doesn't work for $n=1$. Sorry, it doesn't work for all $n in mathbb N$. As of now, $sqrt{23} notin mathbb Z$.
– amWhy
Nov 28 at 22:17
Does it even hold for $n=1$?
– Quang Hoang
Nov 28 at 22:17
sorry i have to remake my question !!
– FADZA
Nov 28 at 22:20
add a comment |
3
It doesn't work for $n=1$. Sorry, it doesn't work for all $n in mathbb N$. As of now, $sqrt{23} notin mathbb Z$.
– amWhy
Nov 28 at 22:17
Does it even hold for $n=1$?
– Quang Hoang
Nov 28 at 22:17
sorry i have to remake my question !!
– FADZA
Nov 28 at 22:20
3
3
It doesn't work for $n=1$. Sorry, it doesn't work for all $n in mathbb N$. As of now, $sqrt{23} notin mathbb Z$.
– amWhy
Nov 28 at 22:17
It doesn't work for $n=1$. Sorry, it doesn't work for all $n in mathbb N$. As of now, $sqrt{23} notin mathbb Z$.
– amWhy
Nov 28 at 22:17
Does it even hold for $n=1$?
– Quang Hoang
Nov 28 at 22:17
Does it even hold for $n=1$?
– Quang Hoang
Nov 28 at 22:17
sorry i have to remake my question !!
– FADZA
Nov 28 at 22:20
sorry i have to remake my question !!
– FADZA
Nov 28 at 22:20
add a comment |
1 Answer
1
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up vote
6
down vote
$n > 0 Rightarrow 1+5^n+6^n+11^n equiv 3 mod 5,$ hence this is never an integer except when $n=0.$
answered Nov 28 at 22:27
Display name
789313
can you please explain to me why did you choose mod 5 !!
– FADZA
Nov 28 at 22:47
1
@awiya I noticed the $5,$ then noticed that $11 equiv 6 equiv 1 bmod 5.$
– Display name
Nov 28 at 22:50
get it ... thank you @Display name
– FADZA
Nov 28 at 22:56
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
6
down vote
$n > 0 Rightarrow 1+5^n+6^n+11^n equiv 3 mod 5,$ hence this is never an integer except when $n=0.$
answered Nov 28 at 22:27
Display name
789313
can you please explain to me why did you choose mod 5 !!
– FADZA
Nov 28 at 22:47
1
@awiya I noticed the $5,$ then noticed that $11 equiv 6 equiv 1 bmod 5.$
– Display name
Nov 28 at 22:50
get it ... thank you @Display name
– FADZA
Nov 28 at 22:56
add a comment |
up vote
6
down vote
$n > 0 Rightarrow 1+5^n+6^n+11^n equiv 3 mod 5,$ hence this is never an integer except when $n=0.$
answered Nov 28 at 22:27
Display name
789313
can you please explain to me why did you choose mod 5 !!
– FADZA
Nov 28 at 22:47
1
@awiya I noticed the $5,$ then noticed that $11 equiv 6 equiv 1 bmod 5.$
– Display name
Nov 28 at 22:50
get it ... thank you @Display name
– FADZA
Nov 28 at 22:56
add a comment |
up vote
6
down vote
up vote
6
down vote
$n > 0 Rightarrow 1+5^n+6^n+11^n equiv 3 mod 5,$ hence this is never an integer except when $n=0.$
answered Nov 28 at 22:27
Display name
789313
$n > 0 Rightarrow 1+5^n+6^n+11^n equiv 3 mod 5,$ hence this is never an integer except when $n=0.$
answered Nov 28 at 22:27
Display name
789313
answered Nov 28 at 22:27
Display name
789313
answered Nov 28 at 22:27
Display name
789313
answered Nov 28 at 22:27
Display name
789313
789313
can you please explain to me why did you choose mod 5 !!
– FADZA
Nov 28 at 22:47
1
@awiya I noticed the $5,$ then noticed that $11 equiv 6 equiv 1 bmod 5.$
– Display name
Nov 28 at 22:50
get it ... thank you @Display name
– FADZA
Nov 28 at 22:56
add a comment |
can you please explain to me why did you choose mod 5 !!
– FADZA
Nov 28 at 22:47
1
@awiya I noticed the $5,$ then noticed that $11 equiv 6 equiv 1 bmod 5.$
– Display name
Nov 28 at 22:50
get it ... thank you @Display name
– FADZA
Nov 28 at 22:56
can you please explain to me why did you choose mod 5 !!
– FADZA
Nov 28 at 22:47
can you please explain to me why did you choose mod 5 !!
– FADZA
Nov 28 at 22:47
1
1
@awiya I noticed the $5,$ then noticed that $11 equiv 6 equiv 1 bmod 5.$
– Display name
Nov 28 at 22:50
@awiya I noticed the $5,$ then noticed that $11 equiv 6 equiv 1 bmod 5.$
– Display name
Nov 28 at 22:50
get it ... thank you @Display name
– FADZA
Nov 28 at 22:56
get it ... thank you @Display name
– FADZA
Nov 28 at 22:56
add a comment |
3
It doesn't work for $n=1$. Sorry, it doesn't work for all $n in mathbb N$. As of now, $sqrt{23} notin mathbb Z$.
– amWhy
Nov 28 at 22:17
Does it even hold for $n=1$?
– Quang Hoang
Nov 28 at 22:17
sorry i have to remake my question !!
– FADZA
Nov 28 at 22:20