All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Factorial Difference = Perfect Square (Posted on 2011-03-28)
Determine all possible pair(s) (x, y) of nonnegative integers such that (x!*y! - x! - y!) is a perfect square.

 No Solution Yet Submitted by K Sengupta Rating: 2.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: possible pairs | Comment 2 of 3 |
(In reply to possible pairs by Dej Mar)

For totals of x + y through 1003, the only sets are (2,2), (2,3) and (3,2):

list
10   for T=0 to 999999
20     for X=0 to int(T/2)
30        Y=T-X
40        Fx=!(X):Fy=!(Y)
50        Tst=Fx*Fy-Fx-Fy
55        if Tst>=0 then
60          :Sr=int(sqrt(Tst)+0.5)
70          :if Sr*Sr=Tst then print X;Y,Tst,Sr
80     next
90   next
OK
run
2  2    0       0
2  3    4       2
Overflow in 60
?t
1004
OK

(The program looks only for y>x, but the puzzle doesn't so require; therefore the solution includes a reversal of a found pair.)

 Posted by Charlie on 2011-03-28 14:29:09

 Search: Search body:
Forums (0)