OFFSET
1,1
COMMENTS
See A261296 for the smaller of the pairs and for additional comments.
REFERENCES
H. E. Dudeney, 536 Puzzles & Curious Problems, Charles Scribner's Sons, New York, 1967, pp 56, 268, #177
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..302
Gianlino, in reply to Smci, Solution method for "integers with the difference between their cubes is a square, and v.v.", Yahoo! answers, 2011
EXAMPLE
(6, 10) is a pair since 10^3 - 6^3 = 784 = 28^2, 10^2 - 6^2 = 64 = 4^3.
PROG
(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))
CROSSREFS
KEYWORD
nonn
AUTHOR
Pieter Post, Aug 15 2015
EXTENSIONS
Added a(6) and more terms added by Chai Wah Wu, Aug 17 2015
STATUS
approved