( 503) 
Ín both columns the addition must be performed at the same 
time; the entire number of additions is only 4, 
Example G = 1677803 = 1296? — 1813. 
Here 0? can end only in 1, so b° — 1818 or p(2a, + p) only 
in 8. 
Of 1 Xx 2593, 2 & 2594, ete. we need but take those, whose first 
factor ends in 2 or 6. 
This gives the operation (at the same time in two columns): 
2>< 2594 +1813=— 6901 | GX 2598 + 1813— 17401 
(2 + 2594) X 10 + 100 = 26060 | (6+2598) x 10-+100= 26140 
32961 43541 
2626 2634 
5922 6988 _ 
2646 2654 
8568 9642 
2666 2674 
11234 12316 | 
2686 2694 
13920 15010 
2706 2714 
166261 177241 = 421? 
from which ensues G = 1362? — 421? 
oh tog >< JEN 
According to the common method of § I 
1362 — 1296 = 66 
numbers ought to have been added; now their number is only 12. 
The additions of the first column are useless and the question 
might be put whether this was not discernible beforehand. 
This is really the case, if we make use of the table of the 4 last 
figures of a square (page 332). 
For b? can terminate only in 1, so a? in 04, 24, 44, 64, 84. 
According to the table a number terminating in 04 can be square 
only when the number formed by thousands und hundreds is a 
4-fold or a 4-fold —1. For shortness’ sake we shall indicate this 
4 
by: Cet 9) 04. If we subtract this number 7803 formed by the 
33* 
