SIR F. POLLOCK ON CERTAIN PROPERTIES OF SQUARE NUMBERS, ETC. 319 
Table of odd numbers and of the Roots of the squares (not exceeding 4) into which 
they may be divided, whose algebraic sum may equal 1. 
Odd 
numbers. 
Roots of the Squares into 
which they may be divided 
whose algebraic sum may equal 1 . 
Odd 
numbers. 
Roots of the Squares into 
which they may he divided 
whose algebraic sum may equal 1. 
Odd 
numbers. 
Roots of the Squares into 
which they may be divided 
whose algebraic sum may equal 1. 
1 
0 
0 
0 
1 
65 
2 
3 
4 
6 
129 
2 
5 
6 
8 
3 
0 
1 
1 
1 
67 
1 
1 
4 
7 
131 
0 
5 
5 
9 
5 
0 
0 
1 
2 
69 
1 
4 
4 
6 
133 
5 
6 
6 
6 
7 
1 
1 
1 
2 
71 
1 
3 
5 
6 
135 
5 
5 
6 
7 
9 
0 
1 
2 
2 
73 
4 
4 
4 
5 
137 
4 
6 
6 
7 
11 
0 
1 
1 
3 
75 
3 
4 
5 
5 
139 
4 
5 
7 
7 
13 
1 
2 
2 
2 
77 
3 
4 
4 
6 
141 
4 
5 
6 
8 
15 
1 
1 
2 
3 
79 
3 
3 
5 
6 
143 
2 
3 
7 
9 
17 
0 
2 
2 
3 
81 
2 
4 
5 
6 
145 
3 
6 
6 
8 
19 
0 
1 
3 
3 
83 
0 
3 
5 
7 
147 
3 
5 
7 
8 
21 
2 
2 
2 
3 
85 
2 
4 
4 
7 
149 
2 
3 
6 
10 
23 
1 
2 
3 
3 
87 
2 
3 
5 
7 
151 
3 
5 
6 
9 
25 
1 
2 
2 
4 
89 
0 
2 
6 
7 
153 
2 
2 
8 
9 
27 
1 
1 
3 
4 
91 
4 
5 
5 
5 
155 
3 
4 
7 
9 
29 
0 
2 
3 
4 
93 
4 
4 
5 
6 
157 
6 
6 
6 
7 
31 
2 
3 
3 
3 
95 
3 
5 
5 
6 
159 
5 
6 
7 
7 
38 
2 
2 
3 
4 
97 
3 
4 
6 
6 
161 
5 
6 
6 
8 
35 
1 
3 
3 
4 
99 
3 
4 
5 
7 
163 
5 
5 
7 
8 
37 
1 
2 
4 
4 
101 
0 
1 
6 
8 
165 
4 
6 
7 
8 
39 
1 
2 
3 
5 
103 
2 
5 
5 
7 
167 
1 
2 
9 
9 
41 
0 
0 
4 
5 
105 
2 
4 
6 
7 
169 
4 
6 
6 
9 
' 43 
3 
3 
3 
4 
107 
1 
3 
4 
9 
171 
4 
5 
7 
9 
45 
2 
3 
4 
4 
109 
2 
4 
5 
8 
173 
1 
6 
6 
10 
47 
2 
3 
3 
5 
111 
5 
5 
5 
6 
175 
3 
6 
7 
9 
49 
2 
2 
4 
5 
113 
4 
5 
6 
6 
177 
4 
5 
6 
10 
51 
1 
3 
4 
5 
115 
4 
5 
5 
7 
179 
3 
5 
8 
9 
53 
2 
2 
3 
6 
117 
4 
4 
6 
7 
181 
1 
4 
8 
10 
55 
1 
3 
3 
6 
119 
3 
5 
6 
7 
183 
6 
7 
7 
7 
57 
3 
4 
4 
4 
121 
2 
2 
7 
8 
185 
6 
6 
7 
8 
59 
3 
3 
4 
5 
123 
3 
5 
5 
8 
187 
5 
7 
7 
8 
61 
2 
4 
4 
5 
125 
3 
4 
6 
8 
189 
5 
6 
8 
8 
63 
2 
3 
5 
5 
127 
1 
3 
6 
9 
191 
5 
6 
7 
9 
