perplexus.info :: Just Math : Positively Positive

Positively Positive (Posted on 2016-10-18)

Find all pairs (A, B) of positive integers such that each of the equations
x² - A*x + B = 0 and x² - B*x + A=0 has positive integer roots.

Prove that there are no others.

Submitted by K Sengupta

Rating: 4.0000 (2 votes)

Solution: (Hide)

The only solutions to the given problem are given by:
(A,B) = (4,4), (5,6), and (6,5)
For an proof that these are the only solutions, refer to the solution submitted by Brian Smith in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Puzzle Thoughts	K Sengupta	2023-12-24 07:26:33
Solution	Brian Smith	2023-12-23 22:12:29
Puzzle Thoughts	K Sengupta	2023-01-01 06:49:35
Part 1 only (spoiler)	Harry	2016-10-19 17:15:01
re: My solution	Steve Herman	2016-10-19 07:11:28
Another way.	broll	2016-10-19 06:19:44
My solution	Ady TZIDON	2016-10-19 01:58:18
צט	Ady TZIDON	2016-10-18 19:05:13
צט	Ady TZIDON	2016-10-18 19:05:13
findings	Charlie	2016-10-18 16:18:25

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