n 1. A unit fraction is a fraction of the form where n is a positive integer. Note that the unit fraction can be written as the sum of two unit fractions in the following three ways: 1 1 1 1 1 + 1 1 + + 11 12 132 22 22 132 12 Are there any other ways of decomposing into the sum of two unit fractions? In how many ways can we write as the sum of two unit fractions? More generally, in how many ways can the unit fraction be written as the sum of two unit fractions? In other words, how many ordered pairs (a, b) of positive integers a, b are there for which n - 1 18 n - 1 1 + = ? a b =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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n
1. A unit fraction is a fraction of the form where n is a positive integer. Note that the
unit fraction can be written as the sum of two unit fractions in the following three
ways:
1
1
+
132 12
Are there any
other ways
1
60
of decomposing into the sum of two unit fractions? In how
many ways can we write as the sum of two unit fractions? More generally, in how
many ways can the unit fraction be written as the sum of two unit fractions? In other
words, how many ordered pairs (a, b) of positive integers a, b are there for which
n
1
11
1
12
+
1
132
1
n
-
1 1
22 22
1 1
a
+ ?
b
Transcribed Image Text:n 1. A unit fraction is a fraction of the form where n is a positive integer. Note that the unit fraction can be written as the sum of two unit fractions in the following three ways: 1 1 + 132 12 Are there any other ways 1 60 of decomposing into the sum of two unit fractions? In how many ways can we write as the sum of two unit fractions? More generally, in how many ways can the unit fraction be written as the sum of two unit fractions? In other words, how many ordered pairs (a, b) of positive integers a, b are there for which n 1 11 1 12 + 1 132 1 n - 1 1 22 22 1 1 a + ? b
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