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A053443 x^2 + y^2 does not take on all possible values mod n. 3
4, 8, 9, 12, 16, 18, 20, 24, 27, 28, 32, 36, 40, 44, 45, 48, 49, 52, 54, 56, 60, 63, 64, 68, 72, 76, 80, 81, 84, 88, 90, 92, 96, 98, 99, 100, 104, 108, 112, 116, 117, 120, 121, 124, 126, 128, 132, 135, 136, 140, 144, 147, 148, 152, 153, 156, 160, 162, 164, 168, 171 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sequence gives values of n such there is not always a solution 1 < z < n to x^2 + y^2 = z (mod n) - Benoit Cloitre, Jan 04 2002; corrected by Carmine Suriano, Jun 19 2013

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

FORMULA

n divisible by p^2 where p = 2 or prime p == 3 (mod 4).

PROG

(PARI) is(n)=my(v=vectorsmall(n, i, 1)); for(x=0, n\2, for(y=0, x, v[(x^2+y^2)%n+1]=0)); vecmax(v) \\ Charles R Greathouse IV, Jun 19 2013

(PARI) is(n)=forprime(p=2, 97, my(o=valuation(n, p)); if(o, if(o>1&&p%4>1, return(1)); n/=p^o)); my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1&&f[i, 1]%4>1, return(1))); 0 \\ Charles R Greathouse IV, Jun 19 2013

CROSSREFS

Cf. A053444.

Sequence in context: A327877 A034043 A278517 * A048098 A322109 A122145

Adjacent sequences:  A053440 A053441 A053442 * A053444 A053445 A053446

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified November 17 08:39 EST 2019. Contains 329217 sequences. (Running on oeis4.)