Template:Sequence of the Day for October 21

Intended for: October 21, 2011

Timetable

• First draft entered by Alonso del Arte on July 24, 2011 ✓
• Draft to be reviewed by August 21, 2011
• Draft to be approved by September 21, 2011

Yesterday's SOTD * Tomorrow's SOTD

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Some Mordell curves in Grapher for Mac OS X.

A081119: Number of integral solutions to Mordell’s equation

y 2 = x 3 + n

.

{ 5, 2, 2, 2, 2, 0, 0, 7, 10, 2, ... }

Mordell’s equation has a finite number of integral solutions for all nonzero

n

. For example, for

n = 1

, there are five solutions: (2, –3), (0, –1), (–1, 0), (0, 1) and (2, 3). For

n = 2

to 5, there are just two solutions each and none for

n = 6

or 7.