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 A254328 Numbers k such that all x^2 mod k are squares (including 0 and 1). 4
 1, 2, 3, 4, 5, 8, 12, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Are there any more terms > 16? There are no more terms less than 10^12. Probably the sequence is finite. - Charles R Greathouse IV, Jan 29 2015 This is a subsequence of A303704, so it is full. - Jianing Song, Feb 14 2019 LINKS EXAMPLE Terms k <= 16 and the squares mod k: 1: [0] 2: [0, 1] 3: [0, 1, 1] 4: [0, 1, 0, 1] 5: [0, 1, 4, 4, 1] 8: [0, 1, 4, 1, 0, 1, 4, 1] 12: [0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1] 16: [0, 1, 4, 9, 0, 9, 4, 1, 0, 1, 4, 9, 0, 9, 4, 1] k = 10 is not a term: in the list of squares mod 10, [0, 1, 4, 9, 6, 5, 6, 9, 4, 1], the numbers 5 and 6 are not squares. MATHEMATICA f[n_] := Mod[Range[n]^2, n]; Select[Range@ 10000, AllTrue[f@ #, IntegerQ[Sqrt[#]] &] &] (* AllTrue function introduced in version 10; Michael De Vlieger, Jan 29 2015 *) PROG (PARI) isok(n)=for(k=2, n-1, if(!issquare(lift(Mod(k, n)^2)), return(0))); return(1); for(n=1, 10^9, if(isok(n), print1(n, ", "))); (PARI) is(n)=for(k=sqrtint(n)+1, n\2, if(!issquare(k^2%n), return(0))); 1 for(m=10, 10^6, for(k=0, sqrtint(2*m), if(is(t=m^2-k^2), print(t)))) \\ Charles R Greathouse IV, Jan 29 2015 CROSSREFS Cf. A065428, A254329, A096008, A303704. Sequence in context: A179402 A065428 A059747 * A094087 A225132 A240216 Adjacent sequences:  A254325 A254326 A254327 * A254329 A254330 A254331 KEYWORD nonn,fini,full AUTHOR Joerg Arndt, Jan 28 2015 EXTENSIONS Keywords fini and full added by Jianing Song, Feb 14 2019 STATUS approved

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Last modified May 18 23:41 EDT 2021. Contains 344009 sequences. (Running on oeis4.)