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Search: id:A120211
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| A120211 |
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x values giving the smallest integer solutions of y^2 = x*(a^N - x)*( b^N + x) (elliptic curve, Weierstrass equation) with a and b legs in primitive Pythagorean triangles and N = 2. Sequence ordered in increasing values of leg a. Relevant y values in A120210. |
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+0
5
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| 4, 6, 12, 24, 15, 40, 60, 40, 70, 84, 72, 56, 126, 144, 180, 168, 198, 180, 220, 264, 126, 286, 312, 364, 360, 390, 420, 480, 510, 49, 544, 300, 612, 616, 646, 684, 720, 760, 288, 798, 840, 924, 726, 966, 700, 1012, 1104, 990, 1150, 1200
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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First primitive Pythagorean triad: 3, 4, 5
Weierstrass equation. y^2 = x*( 3^2 - x)*( 4^2 + x)
Smallest integer solution (x, y) = (4,20)
First element in the sequence x = 4
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MAPLE
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flag :=1; x:=0; # a, b, c primitive Pythagorean triad while flag =1 do x:=x+1; y2:= x*( a^2 - x)*(x+b^2); if ((floor(sqrt(y2)))^2=y2)then print( x); flag :=0; fi; od;
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CROSSREFS
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Cf. A009003, A020884, A120210, A120212, A120213.
Sequence in context: A050558 A098145 A054167 this_sequence A095416 A162688 A070232
Adjacent sequences: A120208 A120209 A120210 this_sequence A120212 A120213 A120214
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KEYWORD
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nonn
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AUTHOR
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Giorgio Balzarotti, Paolo P. Lava (greenblue(AT)tiscali.it), Jun 10 2006
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