Quotients of Siifus and Differences of Perfect Squares 15 



that is by 



i^x ^ — ^(mod 12). 



The smallest positive root of this congruence is 4, hence x is 

 integral for every value 



^\=4+i2\, X = 0,1,2,3 



We have accordingly 



8 100 10000 117 10117 



9 112 12544 131 12675 

 10 124 15376 145 15521 



and finally 



-y|-^'A=^-^\'^i'2>i.i>2^x)- 



369 



