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January 21, 2017
Posted by **frm** on Thursday, October 10, 2013 at 11:07pm.

- Number Theory.,Math -
**Reiny**, Friday, October 11, 2013 at 12:11amclearly (1,1) will work

I then made up and ran a silly little computer program where I let a go from 1 to 1000 and b = 1 to 1000 and tested each case

(so my program tested 1 million cases)

it found the following ordered pairs

1 3 3 1 5 19 7 9 9 7 19 5

testing (19,5)

if a = 19 and b=5

(4a-1)/b = 75/5 = 15 which is an integer

(4b-1)/a = 19/19 = 1 , which is an integer

notice they come in symmetric pairs

so there 7 of these. - Number Theory.,Math -
**Reiny**, Friday, October 11, 2013 at 12:17amI just changed my a values from 1 to 10,000

and my b value from 1 to 10,000

and it found no others.

should have put them in ordered pairs:

(1,1) (1,3) (3,1) (5,19) , (7,9), (9,7), (19,5)