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A070303 Primes p such that the equation p^2*x^2==0 (mod p^2+x^2) has no solution. 3

%I #18 Sep 11 2019 06:59:36

%S 3,7,11,13,19,23,29,31,41,43,47,53,59,61,67,71,73,79,83,89,97,103,107,

%T 109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,199,

%U 211,223,227,229,233,239,241,251,263,269,271,277,281,283,293,307,311

%N Primes p such that the equation p^2*x^2==0 (mod p^2+x^2) has no solution.

%H Amiram Eldar, <a href="/A070303/b070303.txt">Table of n, a(n) for n = 1..10000</a>

%F Primes not in A002496 (i.e., not of the form k^2+1).

%F a(n) ~ n log n. - _Charles R Greathouse IV_, Sep 30 2012

%t Select[Range[320], PrimeQ[#] && !IntegerQ @ Sqrt[# - 1] &] (* _Amiram Eldar_, Sep 11 2019 *)

%o (PARI) for(n=1,350,if(0==sum(i=1,n^2,if((n^2*i^2)%(n^2+i^2),1-isprime(n),1)),print1(n,",")))

%o (PARI) is(n)=isprime(n) && !issquare(n-1) \\ _Charles R Greathouse IV_, Sep 30 2012

%o (PARI) print1(3); forstep(k=2, 9, 2, forprime(p=k^2+3, (k+2)^2, print1(", "p))) \\ _Charles R Greathouse IV_, Sep 30 2012

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, May 10 2002

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Last modified March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)