 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Near Pythagoras (Posted on 2013-07-31) Determine all possible pairs (x,y) of half-integers, with x ≤ y, that satisfy this equation:

[x2] + [y2] = 2016

Prove that there are no others.

*** [x] denotes the greatest integer ≤ x.

 No Solution Yet Submitted by K Sengupta No Rating Comments: ( Back to comment list | You must be logged in to post comments.) computer solution | Comment 1 of 4

10   for X=1 to 5000 step 2
20    for Y=X to 5000 step 2
30       T=int(X*X//4)+int(Y*Y//4)
40       if T=2016 then print X//2,Y//2
50    next
60   next
110   for X=-1 to -10000 step -2
120       Term1=int(X*X//4)
130       Term2=2016-Term1
140       Ysq=Term2+1//4
150       Num=Ysq*4
160       Y=int(sqrt(Num)+0.5)
170       if Y*Y=Num then print X//2,Y//2
180   next

finds

x         y
29/2   85/2
55/2   71/2
-29/2   85/2
-55/2   71/2
-71/2   55/2
-85/2   29/2

before running out of real answers and crashing with:

Illegal parameter in 160

The program uses variables x and y to represent twice x or y.

 Posted by Charlie on 2013-07-31 18:13:43 Please log in:

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