( 506 ) 
and as 75025 is a (4v + 2) 25, we shall have: 
(4 v + 2) 25 According to the table 25 can be preceded 
Gt Den only by a 4-fold or a 4-fold + 2; con- 
(ety on sequently the second column can produce 
“(40 + 2) 25. a square only after addition of successively 
10 numbers. 
To the third column we shall have to add successively : 
5 X 116820, 5 x 117820, 5 X 118820, etc, 
4 
or 584100, 589100, 594100, that isa(4>* 1) 00, 
and as 446225 is a (4v + 2) 25, also this column can produce a 
square only after addition of every time 10 numbers. 
As 28769 of the first column is a (4 v—1)69 and 115700 a 
(4v +1) 00, we shall have successively 
(4v — 1) 69 from which in connection with the table 
(4 + 1) 00 is evident, that only the 2nd, 4th, 6th ete. 
Vite Ane additions can produce squares, so that the 
“(40 — 1) 69 operation becomes: 
= ’ 
2 11558 + 5653 = 28769 
(2 + 11558) & 10 + 100 = 115700 
115900 dua tie 
260369 
2324 
4927 
2332 
7259 
2340 
9599 
2348 
11947 
2356 
14303 
2364 
16667 
ete. 
The numbers 2316, 2324, ete. ascend with 4. Another small 
abbreviation can be brought about by remarking that J? must be 
