In order to determine precisely which are the exceptional numbers, we must consider more particularly the numbers between and for which . For these must be , and
Now in order that (6·41) may be of the form (6·42), must be if is of the form and may have any of the values if is of the form . Thus the only numbers which cannot be expressed in the form (5·2), in this case, are those of the form less than and those of the form
In this case we have to prove that
(i) if , there is an infinity of integers which cannot be expressed in the form (5·2);
(ii) if is , , , or , there is only a finite number of exceptions.
Page:On the expression of a number in the form 𝑎𝑥²+𝑏𝑦²+𝑐𝑧²+𝑑𝑢².djvu/7
Jump to navigation Jump to search
This page has been validated.
in the form