The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A354620

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A354620

Numbers k such that whenever the sum of three squares is divisible by k, at least two of the squares are congruent mod k.
(history; published version)

#43 by Alois P. Heinz at Fri May 12 08:38:11 EDT 2023

STATUS

proposed

approved

#42 by Jean-François Alcover at Fri May 12 08:36:35 EDT 2023

STATUS

editing

proposed

#41 by Jean-François Alcover at Fri May 12 08:36:27 EDT 2023

MATHEMATICA

filter[n_] := Module[{R, i, j, nR, a, b, c}, R = Union@ Table[Mod[i^2, n], {i, 0, n-1}]; nR = Length[R]; For[i = 2, i <= nR, i++, a = R[[i]]; For[j = 1, j <= i-1, j++, b = R[[j]]; c = Mod[-a-b, n]; If[MemberQ[R, c] && c != a && c != b, Return[False]]]]; True];

Select[Range[10000], filter] (* Jean-François Alcover, May 12 2023, after Robert Israel *)

STATUS

approved

editing

#40 by Jon E. Schoenfield at Mon Aug 22 03:59:28 EDT 2022

STATUS

proposed

approved

#39 by Jon E. Schoenfield at Mon Aug 22 03:54:51 EDT 2022

STATUS

editing

proposed

#38 by Jon E. Schoenfield at Mon Aug 22 03:54:48 EDT 2022

LINKS

Mathematics StackExchange, Stack Exchange, <a href="https://math.stackexchange.com/questions/4490010/sum-of-squares-and-quadratc-residues/4490041">Sum of squares and quadratic residues</a>

STATUS

approved

editing

#37 by Michael De Vlieger at Fri Jul 15 08:10:51 EDT 2022

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reviewed

approved

#36 by Michel Marcus at Fri Jul 15 02:40:28 EDT 2022

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proposed

reviewed

#35 by Robert Israel at Fri Jul 15 00:19:07 EDT 2022

STATUS

editing

proposed

#34 by Robert Israel at Fri Jul 15 00:19:02 EDT 2022

EXAMPLE

a(5) = 6 is in the sequence because the solutions to a^2 + b^2 + c^2 == 0 (mod 6) have (up to permutation) [a^2, b^2, c^2] == [0, 0, 0], [0, 3, 3], [1, 1, 4], or [4, 4, 4], all of which have at least two congruent mod 6.

STATUS

proposed

editing