Constrained Divisibility: $n^2+m mid (m-l)^2+(m-k)^2$ [closed]
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Let $n$ be an arbitrary natural number. Let $m,l,k$ be natural numbers, all less than $2n+1$, which satisfy the condition $n^2+m mid (m-l)^2+(m-k)^2$. Find all such triples $(m,l,k)$.
For instance, I found $(1,2,n+1)$ triple.
elementary-number-theory divisibility
edited Nov 23 at 17:51
Martin Sleziak
44.4k7115268
asked Nov 23 at 15:07
Venkaat Balaje
123
closed as off-topic by user302797, Gibbs, amWhy, Leucippus, Cesareo Nov 24 at 1:27
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 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." – user302797, Gibbs, amWhy, Leucippus, Cesareo
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Let $n$ be an arbitrary natural number. Let $m,l,k$ be natural numbers, all less than $2n+1$, which satisfy the condition $n^2+m mid (m-l)^2+(m-k)^2$. Find all such triples $(m,l,k)$.
For instance, I found $(1,2,n+1)$ triple.
elementary-number-theory divisibility
edited Nov 23 at 17:51
Martin Sleziak
44.4k7115268
asked Nov 23 at 15:07
Venkaat Balaje
123
closed as off-topic by user302797, Gibbs, amWhy, Leucippus, Cesareo Nov 24 at 1:27
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 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." – user302797, Gibbs, amWhy, Leucippus, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
On MathOverflow: Interesting Divisibility: $n^2+m mid (m−l)^2+(m−k)^2$
– Martin Sleziak
Nov 23 at 17:52
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
Let $n$ be an arbitrary natural number. Let $m,l,k$ be natural numbers, all less than $2n+1$, which satisfy the condition $n^2+m mid (m-l)^2+(m-k)^2$. Find all such triples $(m,l,k)$.
For instance, I found $(1,2,n+1)$ triple.
elementary-number-theory divisibility
edited Nov 23 at 17:51
Martin Sleziak
44.4k7115268
asked Nov 23 at 15:07
Venkaat Balaje
123
Let $n$ be an arbitrary natural number. Let $m,l,k$ be natural numbers, all less than $2n+1$, which satisfy the condition $n^2+m mid (m-l)^2+(m-k)^2$. Find all such triples $(m,l,k)$.
For instance, I found $(1,2,n+1)$ triple.
elementary-number-theory divisibility
elementary-number-theory divisibility
edited Nov 23 at 17:51
Martin Sleziak
44.4k7115268
asked Nov 23 at 15:07
Venkaat Balaje
123
edited Nov 23 at 17:51
Martin Sleziak
44.4k7115268
asked Nov 23 at 15:07
Venkaat Balaje
123
edited Nov 23 at 17:51
Martin Sleziak
44.4k7115268
edited Nov 23 at 17:51
Martin Sleziak
44.4k7115268
edited Nov 23 at 17:51
Martin Sleziak
44.4k7115268
44.4k7115268
asked Nov 23 at 15:07
Venkaat Balaje
123
asked Nov 23 at 15:07
Venkaat Balaje
123
asked Nov 23 at 15:07
Venkaat Balaje
123
123
closed as off-topic by user302797, Gibbs, amWhy, Leucippus, Cesareo Nov 24 at 1:27
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 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." – user302797, Gibbs, amWhy, Leucippus, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by user302797, Gibbs, amWhy, Leucippus, Cesareo Nov 24 at 1:27
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 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." – user302797, Gibbs, amWhy, Leucippus, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
On MathOverflow: Interesting Divisibility: $n^2+m mid (m−l)^2+(m−k)^2$
– Martin Sleziak
Nov 23 at 17:52
add a comment |
On MathOverflow: Interesting Divisibility: $n^2+m mid (m−l)^2+(m−k)^2$
– Martin Sleziak
Nov 23 at 17:52
On MathOverflow: Interesting Divisibility: $n^2+m mid (m−l)^2+(m−k)^2$
– Martin Sleziak
Nov 23 at 17:52
On MathOverflow: Interesting Divisibility: $n^2+m mid (m−l)^2+(m−k)^2$
– Martin Sleziak
Nov 23 at 17:52
add a comment |
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On MathOverflow: Interesting Divisibility: $n^2+m mid (m−l)^2+(m−k)^2$
– Martin Sleziak
Nov 23 at 17:52