28 



L. EULERI OPERA POSTHUMA. 



Arithmettca. 



231. Si divisor d = 7, erit ^ = 6 totidemque habentur casus 



6=1 6 = 2 6 = 3 



Progr. geom. 1, 1 1, 2, 2^ 2» 1, 3, 3^ 3», 3% 3', 3* 



Residua 1, 1 1, 2, *, 1 1, 3, 2, 6, k, 5, 1 



n = l /1 = 3 /1 = 6 



6 = ^ 

 1, A^, ^^ k^ 

 1, 4, 2, 1 



/1 = 3 



6 = 5 

 Progr. geom. 1, 5, 5^ 5^ 5% 5', 5' 

 Residua 1, 5, ft-, 6, 2, 3, 1 



/1 = 6 



6=6 

 i, 6, 6^ 

 1, 6, 1 



/1 = 2 



232. Si divisor ti = 8 , erit ^=k totidemque casus 



6 = 1 6 = 3 6 = 5 



Prog. geom. 1, 1 1, 3, 3* 1, 5, 5* 



Residua 1, 1 1, 3, 1 1, 5, 1 



n= I /1 = 2 /1 = 2 



1 1 



nuUo ergo casu erit w = ^, sed tribus /i=— //, et uno casu n=~/u. 



233. Si divisor sit (i = 9, erit ^ = 6 totidemque casus 



6 = 7 

 1, 7, 7» 

 1, 7, 1 



/1 = 2 



23*. Si sit divisor rf=10, erit ^ = 4 



6 = 1 6 = 3 



Progr. geom. 1, 1 1, 3, 3% 3*, 3* 



Residua 1, 1 1, 3, 9, 7, 1 



/1=1 /1 = 4" 



6 = 7 

 1, 7, 1\ 7«, 7* 

 1, 7, 9, 3, 1 



71 = 4 



6 = 9 

 i, 9, 9* 

 1, 9, 1 



/1 = 2 



235. Sit d = 



6 = 

 Progr. geom. 1, 

 Residua i , 



n = 



1 , erit /u= iO totidemque casus 



6 = 2 

 1, 2, 2^ 2^ 2*, 2*, 2^ 2', 2», 2\ 2'<' 

 1, 2, 4, 8, 5, 10, 9, 7, 3, 6, 1 



/1 = 10 



6 = 3 

 1, 3, 3», 3», 3*, 3' 

 1, 3, 9, 5, k, 1 



/1=5 



