Question

How may ordered pairs of natural numbers (a, x) satisfy ax = a + 4x ?

Answer 1

Given :  ax = a + 4x

To Find : How may ordered pairs of natural numbers (a, x) satisfy

Solution:

ax = a + 4x

=> a(x - 1)  = 4x

=> a  =   4x/(x - 1)

x and x - 1 are consecutive numbers hence co prime

so (x - 1) must  be a factor of 4

Factors of 4 = 1  ,  2  , 4

x -  1  = 1 => x = 2       => a = 8

x - 1  = 2  => x = 3     => a  = 6

x - 1 = 4  => x  = 5     => a  = 5

( 8 , 2)  , ( 6 , 3)  , ( 5 , 5)

three ordered  pairs of natural numbers (a, x) satisfy ax = a + 4x

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