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Sum of Squares, Distinct Primes 
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#1
Nov1210, 01:44 AM

P: 43

Hi All,
So I was just wondering if there is a formula for the number of ways a number can be written as a sum of squares?(Without including negatives, zero or repeats). For example 5=2^2+1^2. (There is only one way for 5). Second question along this line is: In how many ways can a number be written as a sum of primes(i.e a sum of two primes, three primes ). Third Question: 10=2+3+5 Thus 10 can be written as a sum of maximum three prime numbers; no more. Is there such an upper bound for other numbers? I was doing this for small numbers but would be interesting to see if there is some sort of pattern or theory Thanks a lot Abiyo 


#2
Nov1210, 02:16 PM

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P: 3,682

http://mathworld.wolfram.com/SumofSquaresFunction.html http://oeis.org/A000607 


#3
Nov1210, 02:34 PM

P: 43

Thanks CRGreatHouse. Sorry the last question is worded badly. What I wanted to ask is
Pick an integer n. We want to find partition of n into its prime parts. For example 10=7+3 10=2+3+5 There are two partitions of 10 into primes. The first one involves two primes, the second involves three primes. The claim then is that 3 is the maximum partition of 10 into primes. 3 is the longest partition. Now let me choose some arbitrary integer(large n). I might have x number of partitions of n into prime parts. I want to determine the longest partition. (how many prime numbers are involved at maximum). Is there a formula or a theoretical treatment? Thanks a lot once again (My English is terrible. sorry if this is confusing again) 


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