( 505 ) 
(Av + 2) O1 
_ (do + 1)40 
(Av — 1) 41 
4v—l)40 3 
ter 251 ¥ Only the numbers marked with an as- 
(4v + 1) 40 terisk can be squares and the operation 
pide jae can become: 
(4 v — 1) 40 
- (4v—1)61* 6 X 2598 + 1813 = 17401 
(4.0 EN 26140 + 26340 = 52480 
440+ 101 69881 
(Av — 1) 40 53280 
(40 ayer 123161 
(Av + 1) 40 54080 
(&v + ID 81 177241 = 4212 
(4v—1)40_ 
(40+ 1)21* with only three additions. 
(Av + 1) 41 
(4 v + 2) 61 
(4v—1)40 
(40 + 2) 01. * 
Example: G = 33379631 = 5178? — 5653, 
Now a? can terminate only in 00 or 56, 0? in 69 or 25, and p (2a, + p) 
iw: 56. or 92: 
The terminal figure of p can be only 2, 6 or 8 and we have 
2 >< 11558 + 5653—= 28769 6 X 11562 + 5653 == 75035 
(2 + 11558) x 10 +100 = 115700 | (6 + 12562) x 10 + 100 = 115780 
144469 
8 < 11564 +5653 = 98165 
(8 + 11564) X 10 + 100 = 115820 
116020 
116220 
“446225 
The sums of the second and third columns must always have 
25 as terminal figures, so that we shall be able to add 5 numbers 
at a time. 
So we must add to the second column: 
5 x 116180, 5 x 117180, 5 x 118180, ete., 
teke ast 
or 580900, 585900, 590900, that is a Gis: ) 00, 
