- **enzocreti**
(*https://www.mersenneforum.org/forumdisplay.php?f=156*)

- - **51+163k**
(*https://www.mersenneforum.org/showthread.php?t=25210*)

51+163knumbers of the form 51+163k
conjecture 51+163k is a square only for k=10 |

[CODE]for(k=1,10^10,if(issquare(51+163*k),print(k)))
10 91 255 498 826 1231 1723 2290 2946 3675 4495 5386 6370 7423 8571 9786 11098 12475 13951 15490 17130 18831 20635 22498 24466 26491 28623 30810 33106 ... ... [/CODE] Yes infinitely many lol |

Enzo, here is some relevant maths to what you have posted here:
The number 51, in your case, you were testing to see whether it was a quadratic residue (mod 163), that is, whether or not there is a square that is 51 (mod 163). There is a well-known theorem that states that if a number b is a quadratic residue (mod N), then there are infinitely many squares that are b (mod N). In this case, you found that for k=10, there is a square of the form k*N+b for N=163, b=51, therefore 51 is a quadratic residue (mod 163), and there are infinitely many squares of this form using the above theorem. |

[QUOTE=Batalov;537236][
Yes infinitely many lol[/QUOTE] [COLOR="DarkRed"]@ enzocreti - Do not edit other peoples posts.[/COLOR] |

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