Tuesday

September 16, 2014

September 16, 2014

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)

**Answer this Question**

**Related Questions**

number theory, math - How many ordered pairs of positive integers (a,b) are ...

maths - For how many ordered pairs of positive integers n and k with n and k ...

maths - For how many ordered pairs of positive integers n and k with n and k ...

math - Find the sum of all positive integers m such that 2^m can be expressed as...

plls heeeeeeelp math - How many ordered pairs of positive integers 1≤k&#...

heeeeeeeeelp math - How many ordered pairs of positive integers 1≤k≤...

math - How many ordered pairs of positive integers 1≤k≤n≤50 ...

algebra - How many pairs of integers (not necessarily positive) are there such ...

algebra - How many pairs of integers (not necessarily positive) are there such ...

algebra - How many pairs of integers (not necessarily positive) are there such ...