Mixing
Expressing integers as summations
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I've been trying to reduce the visual size of integers with up to a thousand digits by representing them with the summation operator. The only thing I've found that might be somewhat useful is some code that can find a sum of consecutive numbers equal to a given number, but I don't have the experience with this type of math I'd need to make that do what I actually want.
Say I have this equation:
$$sum_{i=x}^y i^z = w$$
I have several questions for this. Given a positive integer w:
- How do I find integer values for x, y and z where the differences between x, y and z are as low as possible? In other words, how do I make the number of digits in x, y and z as evenly distributed as possible?
- How do I determine if there exist integer values for x, y and z that don't have differences of over about a million? If there are none, how can I find an amount to add to or subtract from w that will bring the differences below a million?
- Would these procedures be simple enough to implement in Python or Java?
summation integers programming
asked Jan 19 at 7:43
WellDressedAnonWellDressedAnon
1
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add a comment |
$begingroup$
I've been trying to reduce the visual size of integers with up to a thousand digits by representing them with the summation operator. The only thing I've found that might be somewhat useful is some code that can find a sum of consecutive numbers equal to a given number, but I don't have the experience with this type of math I'd need to make that do what I actually want.
Say I have this equation:
$$sum_{i=x}^y i^z = w$$
I have several questions for this. Given a positive integer w:
- How do I find integer values for x, y and z where the differences between x, y and z are as low as possible? In other words, how do I make the number of digits in x, y and z as evenly distributed as possible?
- How do I determine if there exist integer values for x, y and z that don't have differences of over about a million? If there are none, how can I find an amount to add to or subtract from w that will bring the differences below a million?
- Would these procedures be simple enough to implement in Python or Java?
summation integers programming
asked Jan 19 at 7:43
WellDressedAnonWellDressedAnon
1
$endgroup$
$begingroup$
Most integers will have representations of this type only when $z=1$.
$endgroup$
– Greg Martin
Jan 19 at 7:51
add a comment |
$begingroup$
I've been trying to reduce the visual size of integers with up to a thousand digits by representing them with the summation operator. The only thing I've found that might be somewhat useful is some code that can find a sum of consecutive numbers equal to a given number, but I don't have the experience with this type of math I'd need to make that do what I actually want.
Say I have this equation:
$$sum_{i=x}^y i^z = w$$
I have several questions for this. Given a positive integer w:
- How do I find integer values for x, y and z where the differences between x, y and z are as low as possible? In other words, how do I make the number of digits in x, y and z as evenly distributed as possible?
- How do I determine if there exist integer values for x, y and z that don't have differences of over about a million? If there are none, how can I find an amount to add to or subtract from w that will bring the differences below a million?
- Would these procedures be simple enough to implement in Python or Java?
summation integers programming
asked Jan 19 at 7:43
WellDressedAnonWellDressedAnon
1
$endgroup$
I've been trying to reduce the visual size of integers with up to a thousand digits by representing them with the summation operator. The only thing I've found that might be somewhat useful is some code that can find a sum of consecutive numbers equal to a given number, but I don't have the experience with this type of math I'd need to make that do what I actually want.
Say I have this equation:
$$sum_{i=x}^y i^z = w$$
I have several questions for this. Given a positive integer w:
- How do I find integer values for x, y and z where the differences between x, y and z are as low as possible? In other words, how do I make the number of digits in x, y and z as evenly distributed as possible?
- How do I determine if there exist integer values for x, y and z that don't have differences of over about a million? If there are none, how can I find an amount to add to or subtract from w that will bring the differences below a million?
- Would these procedures be simple enough to implement in Python or Java?
summation integers programming
summation integers programming
asked Jan 19 at 7:43
WellDressedAnonWellDressedAnon
1
asked Jan 19 at 7:43
WellDressedAnonWellDressedAnon
1
asked Jan 19 at 7:43
WellDressedAnonWellDressedAnon
1
asked Jan 19 at 7:43
WellDressedAnonWellDressedAnon
1
asked Jan 19 at 7:43
WellDressedAnonWellDressedAnon
1
1
$begingroup$
Most integers will have representations of this type only when $z=1$.
$endgroup$
– Greg Martin
Jan 19 at 7:51
add a comment |
$begingroup$
Most integers will have representations of this type only when $z=1$.
$endgroup$
– Greg Martin
Jan 19 at 7:51
$begingroup$
Most integers will have representations of this type only when $z=1$.
$endgroup$
– Greg Martin
Jan 19 at 7:51
$begingroup$
Most integers will have representations of this type only when $z=1$.
$endgroup$
– Greg Martin
Jan 19 at 7:51
add a comment |
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$begingroup$
Most integers will have representations of this type only when $z=1$.
$endgroup$
– Greg Martin
Jan 19 at 7:51