How-many-pairs-of-integers-x-and-y-satisfy-the-equation-1-x-1-y-1-32-

Question Number 110592 by Aina Samuel Temidayo last updated on 29/Aug/20

How many pairs of integers x and y

satisfy the equation \frac{1}{x} + \frac{1}{y} = \frac{1}{32}

Answered by Aziztisffola last updated on 29/Aug/20

if x = y \Rightarrow \frac{2}{x} = \frac{1}{32} \Rightarrow x = 64

(x; y) = (64; 64) \in S then S \neq \emptyset

there is at least one solution .

Answered by mr W last updated on 29/Aug/20

\frac{1}{y} = \frac{1}{32} - \frac{1}{x} = \frac{x - 32}{32 x}

y = \frac{32 x}{x - 32}

x = 33 \Rightarrow y = 1056

x = 34 \Rightarrow y = 544

x = 36 \Rightarrow y = 288

x = 40 \Rightarrow y = 160

x = 48 \Rightarrow y = 96

x = 64 \Rightarrow y = 64

x = 31 \Rightarrow y = - 993

x = 30 \Rightarrow y = - 480

x = 28 \Rightarrow y = - 224

x = 24 \Rightarrow y = - 96

x = 16 \Rightarrow y = - 32

\dots \dots

Commented by Aina Samuel Temidayo last updated on 29/Aug/20

Thanks but how did you know the values of (x, y)

that fits the equation ? Your work is

not well explanatory .

Commented by mr W last updated on 29/Aug/20

i f x - 32 d i v i d e s 32, t h e n x i s o k .

\Rightarrow x - 32 = \pm 1, \pm 2, \pm 4, \pm 8, \pm 16, \pm 32

Answered by floor(10²Eta[1]) last updated on 29/Aug/20

go see my answer on Q . 103093

{it}^{'} s the same logic

Commented by Aina Samuel Temidayo last updated on 29/Aug/20

Thanks .