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Integer Divisibility Dilemma (Posted on 2014-04-10) Difficulty: 2 of 5
Find all positive integers X and Y such that:
  • X divides Y+5, and:
  • Y divides X+3
Prove that there are no others.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Any with sum of x and y under 10000--no proof of completeness | Comment 3 of 6 |

OPEN "int div dilemma.txt" FOR OUTPUT AS #2
FOR tot = 2 TO 9999
    FOR x = 1 TO tot - 1
        y = tot - x
        IF (y + 5) MOD x = 0 AND (x + 3) MOD y = 0 THEN
            PRINT x, y
            PRINT #2, x, y
        END IF
    NEXT
NEXT
close

finds only

 x             y
 
 1             1
 1             2
 2             1
 3             1
 1             4
 2             5
 6             1
 7             2
 4             7
 9             4
 8             11
 13
            8

  Posted by Charlie on 2014-04-10 11:58:58
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