158 MATHÉMATIQUES, ASTRONOMIE, GÉODÉSIE ET MÉCANIQUE 



pour abréger, au lieu de retrancher les carrés, retranchons les nombres 

 impairs 1, 3, 5, 7... 



n—t-^ IH. 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 

 100, 99, 98, 97, 96, 95, 94. 



aJrt= 11"^^ lli' 11^' 11<'>' '^1^' 11^' 11^' 1"^<^' 121' 1'^-' 1^'^' 

 124, 123, 126, 127, 128, 129, 130. 



±,;. _r-) ^ 182. 179, 174, 167, 158, 147, 134, 119, 10^2, 83, 62, 



.SÇ)^ U, —13, —42, —73, —106, —141. 



Les nombres 94 et 141 ont le commun diviseur 47, qui divisera néces- 

 sairement 12.361. 



Cette méthode paraît être plus expéditive que l'ancienne méthode 

 d'Eratosthène. 



TABLE DES RÉSIDUS QUADRATIQUES. 



3 1. 



3 1, 4. 



7 1, 4, 2. 



11 1, 4, 9, 5, 3. 



13 1, 4, 9, 3, 12, 10. 



17 l, 4, 9, 16, 8, 2, lo, 13. 



19 1, 4, 9, 16, 6, 17, 11, 7, o. 



Plus loin, les résidus carrés ne seront pas écrits. 



23 2, 13, 3, 18, 12, 8, 6. 

 29 7, 20, 6, 23, 13, 5, 28, 24, 22. 

 ^31 S, 18, 2, 19, 7, 28, 20, 14, 10, 8. 

 37 12, 27, 7, 26, 10, 33, 21, H, 3, 34, 30, 28. 

 41 8, 23, 40, 18, 39, 21, 3, 32, 20, 10, 2, 37, 33, 31. 

 43 6, 21, 38, 14, 35, 15, 40, 24, 10, 41, 31, 23, 17, 13, 11. 

 47 2, 17, 34, 6, 27, 3, 28, 8, 37, 21, 7, 42, 32, 24, 18, 14, 12. 

 nS 11, 28, 47, 13, 38, 10, 37, 13, 44, 24, 6, 43, 29, 17, 7, 52, 46, 42, 



iO. 

 69 5, 22, 41, 3, 26, 51, 19, 48, 20, 53, 29, 7, 46, 28, 12, 57, 45, 33, 



27, 21, 17, 15. 

 61 3, 20, 39, 60, 22, 47, 13, 42, 12, 45, 19, 56, 34, 14, 57, 41, 27, 15, 



5, 58, 52, 48, 46. 

 67 14, 33, 54, 10, 35, 62, 24, 35, 21, 56, 26, 65, 39, 15, 60, 40, 22, 6, 



39, 47, 37, 29, 23, 19, 17. 



71 10, 29, 50, 2, 27, 54, 12, 43, 5, 40, 6, 45, 15, 38, 32, 8, 37, 37, 



19, 3, 60, 48, 38, 30, 24, 20, 18. 

 73 8, 27, 48, 71, 23, 50, 6, 37, 70, 32, 69, 35, 3, 46, 18, 65, 41, 19, 



72, 54, 38, 24, 12, 2, 67, 61, 37, 53. 



79 2, 21, 42, 65, 11, 38, 67, 19, 52, 8, 45, 5, 46, 10, 35^ 23, 72, 44, 



18, 73, 51, 31, 13, 76, 62, 30, 40, 32, 26, 22, 20. 



83 17, 38, 61, 3, 30, 59, 7, 40, 75, 29, 68, 26, 69, 31, 78, 44, 12, 65, 



37, 11, 70, 48, 28, 10, 77, 63, 51, 41, 33, 27, 23, 21. 



