Verify that the Diophantine equation x² + y² where d'(n) and d"(n) are the numbers of positive divisors of the form 4k +1 and 4k – 1, of the positive integer n. = n has 4d'(n) – 4d"(n) solutions

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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8. Verify that the Diophantine equation x? + y?
where d'(n) and d"(n) are the numbers of positive divisors of the form 4k +1 and
4k – 1, of the positive integer n.
= n has 4d'(n) – 4d"(n) solutions
Transcribed Image Text:8. Verify that the Diophantine equation x? + y? where d'(n) and d"(n) are the numbers of positive divisors of the form 4k +1 and 4k – 1, of the positive integer n. = n has 4d'(n) – 4d"(n) solutions
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