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A147854 Positive integers n such that n^2 = (x^4 - y^4)*(z^4 - t^4) where the pairs of integers (x,y) and (z,t) are not proportional. 3
520, 975, 2040, 2080, 3567, 3900, 4680, 7215, 7800, 8160, 8320, 8775, 9840, 13000, 13920, 14268, 15600, 18360, 18720, 19680, 24375, 25480, 28860, 30160, 31200, 32103, 32640, 33280, 35100, 39360, 40545, 42120, 47775, 51000, 52000, 53040 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Positive integers n such that n^2 = s^4*A147858(m)*A147858(k) for positive integers s and k<m. If n belongs to this sequence then so does n*s^2 for any positive integer s. Primitive elements of this sequence are given by A147856.

Euler proved that if n^2 = (x^4 - y^4)*(z^4 - t^4) then a,b,c (if n is even) or 4a,4b,4c (if n is odd) form a triple of integers with all pairwise sums and differences being squares, where a=(x^4+y^4)*(z^4+t^4)/2, b=(n^2+(2xyzt)^2)/2 and c=(n^2-(2xyzt)^2)/2. Note that a,b,c are pairwise distinct if and only if (x,y) and (z,t) are not proportional.

LINKS

Table of n, a(n) for n=1..36.

CROSSREFS

Cf. A147856, A147857, A147858.

Sequence in context: A250768 A043626 A235274 * A147856 A094903 A250693

Adjacent sequences:  A147851 A147852 A147853 * A147855 A147856 A147857

KEYWORD

nonn

AUTHOR

Max Alekseyev, Nov 17 2008, Nov 19 2008

STATUS

approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)