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A261328
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Larger of pairs (m, n), such that the difference of their squares is a cube and the difference of their cubes is a square.
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3
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10, 640, 7290, 8954, 40960, 52728, 55566, 70434, 156250, 405000, 466560, 536250, 573056, 960089, 997920, 1176490, 2037960, 2621440, 3374592, 3556224, 3748745, 4379424, 4507776, 5005000, 5314410, 6527466, 6742450, 7778106, 8938800, 10000000, 10214145, 12065355
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OFFSET
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1,1
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COMMENTS
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See A261296 for the smaller of the pairs and for additional comments.
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REFERENCES
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H. E. Dudeney, 536 Puzzles & Curious Problems, Charles Scribner's Sons, New York, 1967, pp 56, 268, #177
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LINKS
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EXAMPLE
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(6, 10) is a pair since 10^3 - 6^3 = 784 = 28^2, 10^2 - 6^2 = 64 = 4^3.
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PROG
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(PARI) is(n)=forstep(k=n-1, 1, -1, issquare(n^3-k^3)&&ispower(n^2-k^2, 3)&&return(k)) \\ M. F. Hasler, Aug 17 2015
(Python)
from __future__ import division
from sympy import divisors
from gmpy2 import is_square
alist = []
for i in range(1, 10000):
c = i**3
for d in divisors(c, generator=True):
d2 = c//d
if d >= d2:
m, r = divmod(d+d2, 2)
if not r:
n = m-d2
if n > 0 and (m, n) not in alist and is_square(c*m+d2*n**2):
alist.append((m, n))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Added a(6) and more terms added by Chai Wah Wu, Aug 17 2015
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STATUS
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approved
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