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Hi

I stumbled across a power series pattern while working on a C algorithm and was wondering if this "discovery" has a name/reference anywhere.

Basically, Here's what I found:

for p = 1 the minimum number of terms, on the left side, satisfying the following is 1

a^p + b^p + c^p ... = m^p

for p = 2 the minimum number of terms, on the left side, satisfying the following is 2

a^p + b^p + c^p ... = m^p (pythagorean theorum)

for p = 3 the minimum number of terms, on the left side, satisfying the following is 3

a^p + b^p + c^p ... = m^p

for p = 4 the minimum number of terms, on the left side, satisfying the following is 5

a^p + b^p + c^p ... = m^p

for p = 5 the minimum number of terms, on the left side, satisfying the following is 6

a^p + b^p + c^p ... = m^p

I wasn't able to take it any farther than this as even on a 2.16 GHz core duo, my brute force method ran for almost a half hour without returning.

So the minimum terms form the sequence 1, 2, 3, 5, 6, ?, ?, ?. I tried looking it up on Sloan's encyclopedia of integer http://www.research.att.com/~njas/sequences/?q=1%2C+1%2C2%2C3%2C5%2C6&sort=0&fmt=0&language=english&go=Search" [Broken] but the small number of terms gave multiple hits.

Is this pattern known? And if so, what is it called? Is there a generating function for it?

Thanks in advance.

Ken

I stumbled across a power series pattern while working on a C algorithm and was wondering if this "discovery" has a name/reference anywhere.

Basically, Here's what I found:

for p = 1 the minimum number of terms, on the left side, satisfying the following is 1

a^p + b^p + c^p ... = m^p

for p = 2 the minimum number of terms, on the left side, satisfying the following is 2

a^p + b^p + c^p ... = m^p (pythagorean theorum)

for p = 3 the minimum number of terms, on the left side, satisfying the following is 3

a^p + b^p + c^p ... = m^p

for p = 4 the minimum number of terms, on the left side, satisfying the following is 5

a^p + b^p + c^p ... = m^p

for p = 5 the minimum number of terms, on the left side, satisfying the following is 6

a^p + b^p + c^p ... = m^p

I wasn't able to take it any farther than this as even on a 2.16 GHz core duo, my brute force method ran for almost a half hour without returning.

So the minimum terms form the sequence 1, 2, 3, 5, 6, ?, ?, ?. I tried looking it up on Sloan's encyclopedia of integer http://www.research.att.com/~njas/sequences/?q=1%2C+1%2C2%2C3%2C5%2C6&sort=0&fmt=0&language=english&go=Search" [Broken] but the small number of terms gave multiple hits.

Is this pattern known? And if so, what is it called? Is there a generating function for it?

Thanks in advance.

Ken

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