RATIONAL POINTS ON SOME FERMAT CURVES AND SURFACES OVER FINITE FIELDS
2014 ◽
Vol 10
(02)
◽
pp. 319-325
◽
Keyword(s):
We give an explicit description of the 𝔽qi-rational points on the Fermat curve uq-1 + vq-1 + wq-1 = 0, for i ∈{1, 2, 3}. As a consequence, we observe that for any such point (u, v, w), the product uvw is a cube in 𝔽qi. We also describe the 𝔽q2-rational points on the Fermat surface uq-1 + vq-1 + wq-1 + xq-1 = 0, and show that the product of the coordinates of any such point is a square.
2017 ◽
Vol 16
(03)
◽
pp. 1750046
Keyword(s):
2012 ◽
Vol 08
(04)
◽
pp. 1087-1097
◽
Keyword(s):
2007 ◽
Vol 13
(3)
◽
pp. 546-562
◽
2001 ◽
Vol 63
(3)
◽
pp. 393-406
Keyword(s):
2015 ◽
Vol 11
(08)
◽
pp. 2405-2430
◽
Keyword(s):
2006 ◽
Vol 73
(2)
◽
pp. 245-254
◽
Keyword(s):
2020 ◽
Vol 21
(1)
◽
pp. 1-51
2013 ◽
Vol 133
(4)
◽
pp. 1194-1206
◽