-- Cheking the last Fermat's theorem
--
-- Thanks Google for today's doodle that bring to my mind 
-- the last Fermat's Theorem.
--
-- This is a small dumb try to catch an error on the theory, 
-- It crash on the wall because quickly reach the higher integer 
-- value, and never gets a cubic sum.
--
-- Is nice to see how many cases of square sum exist, there are 
-- a lot of them, there are several couples of squares that produces 
-- the same sum.
--
-- Please someone try to use an arbitrary values library.
--
--
-- Marco Achury
-- August 17, 2011
-- Released to public domain
--

sequence powers
object junk
integer SquareSum
integer CubicSum
integer Number


powers={}
Number=814  -- 814 is the highest number we can test without error

puts(1,"Filling powers table\n")

for i=1  to Number by 1 do
    powers=append(powers,{i,power(i,2), power(i,3)})
end for

-- Just for debug
-- print(1,powers)

puts(1,"\nChecking values\n")


for i=3  to Number do

-- For debug only
-- print(1,i)
-- puts(1,"\n")

    for j=1  to i-2 do
	for k=j+1 to i-1 do

	    SquareSum=powers[j][2]+powers[k][2]
	    CubicSum=powers[j][3]+powers[k][3]
	
	    if SquareSum = powers[i][2] then
		printf(1,"Found a square sum %3d^2 = %3d^2 + %3d^2 \n",{i,j,k})
	    end if
	    
	    if CubicSum = powers[i][3] then
		
		printf(1,"Found a cubic sum %3d, %3d, %3d\n",{i,j,k})
		puts (1, "Press Enter...")
		junk=gets(0)
		abort(1)
		
	    end if	
	
	end for
    end for

    -- Partial output, non stop comment this block
    if remainder(i,20)=0 then    
        puts (1, "Press Enter... \n")
        junk=gets(0)
    end if
    -- End of partial output

end for

puts (1, "Appear that no cubic sum was found\n")
puts (1, "Press Enter... ")
junk=gets(0)