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Find all solutions to 1/a - 1/b = 1/12 in positive integers.

 Nov 25, 2019
 #1
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+1

a=125; b=100;c=1/a - 1/b; if(c==1/12, goto4, goto5);printa, b; a--;if(a>1, goto2, 0);a=125;b--;if(b>1, goto2, discard=0;

 

a             b
10          60
9            36
8            24
6            12
4             6
3             4

 Nov 25, 2019
 #2
avatar+105476 
+1

1/a  - 1/b  = 1/12

 

(a)   Note that....if this is true, then   0 < a < 12     where a is an integer

 

[ b - a ] / ab  =  1/12

 

12 [ b - a]  =  ab

 

12b - 12a = ab

 

12b - ab  = 12a

 

b  [ 12 - a ]  =  12a

 

b =    12 a / [ 12 - a  ]

 

a = 3     b  =  4

a = 4     b =   6

a = 6     b =  12

a = 8     b = 24

a = 9     b =  36

a  = 10  b =  60

a = 11   b =  132

 

We can stop here because of  the provision of  (a)  

 

 

cool cool cool

 Nov 26, 2019

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