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A178786
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Express n as the sum of four squares, x^2+y^2+z^2+w^2, with x>=y>=z>=w>=0, maximizing the value of x. Then a(n) is that x.
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4
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0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 3, 4, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 7, 8, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 9, 10, 10, 10, 10, 10, 10, 10, 9, 10
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OFFSET
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0,5
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COMMENTS
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Lagrange's theorem tells us that each positive integer can be written as a sum of four squares.
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LINKS
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PROG
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(Python)
from math import *
for nbre in range(0, 500): # or more than 500 !
maxc4=0
for c1 in range(0, int(sqrt(nbre/4))+1):
for c2 in range(c1, int(sqrt(nbre/3))+1):
for c3 in range(c2, int(sqrt(nbre/2))+1):
s3=c3**2+c2**2+c1**2
if s3<=nbre:
c4=sqrt(nbre-s3)
if int(c4)==c4 and c4>=c3:
if c4>maxc4:
maxc4=int(c4)
print(maxc4, end=', ')
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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