A122986 Squares mod 1000.
0, 1, 4, 9, 16, 24, 25, 36, 41, 44, 49, 56, 64, 76, 81, 84, 89, 96, 100, 104, 116, 121, 124, 129, 136, 144, 156, 161, 164, 169, 176, 184, 196, 201, 204, 209, 216, 224, 225, 236, 241, 244, 249, 256, 264, 276, 281, 284, 289, 296, 304, 316, 321, 324, 329, 336, 344
Offset: 1
Examples
The last three digits of n^2 can be 000, 001, 236, 241, 996, etc. but not 002, 003, 237, 238, etc.
Links
- R. Zumkeller, Table of n, a(n) for n = 1..159 (full sequence)
- Eric Weisstein's World of Mathematics, Square Numbers.
- Index entries for sequences related to final digits of numbers
Crossrefs
Programs
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Magma
[n: n in [0..999] | IsSquare(R! n) where R:= ResidueClassRing(1000)]; // Vincenzo Librandi, Dec 29 2019
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Maple
s:={}: for n from 0 to 999 do s:=s union {n^2 mod 1000}: od: op(s); # Nathaniel Johnston, Jun 22 2011 -
Mathematica
Union[PowerMod[Range[1000], 2, 1000]] (* Vincenzo Librandi, Dec 29 2019 *)
Extensions
More terms and additional comments from Reinhard Zumkeller, Mar 21 2010
Edited by N. J. A. Sloane, Apr 10 2010
Comments