' Puzzlet #045
' Find two different integers, both less
' than 100, such that the difference of
' their squares is a perfect cube, and the
' difference of their cubes is a perfect
' square.
' By Dave Ellis.

declare DiffSquaresIsCube(a: int, b: int)
declare DiffCubesIsSquare(a: int, b: int)
declare PrintResult()
def it1, it2: int
openconsole
print "Searching ...": print

for it1 = 1 to 98
    for it2 = it1 + 1 to 99
        if DiffSquaresIsCube(it1, it2)
            if DiffCubesIsSquare(it1, it2)
                PrintResult()
            endif
        endif
    next it2
next it1

print: print "No more!"
print: print "Press a key to exit ... ",
do: until inkey$ <> ""
closeconsole
end

sub DiffSquaresIsCube(a, b)
' if b^2 - a^2 is a perfect cube,
' returns 1, otherwise returns 0
def flag: int
def c: float
c = (b^2 - a^2)^(1/3)
if c = int(c)
    flag = 1
else
    flag = 0
endif
return flag

sub DiffCubesIsSquare(a, b)
' if b^3 - a^3 is a perfect square,
' returns 1, otherwise returns 0
def flag: int
def c: float
c = sqrt(b^3 - a^3)
if c = int(c)
    flag = 1
else
    flag = 0
endif
return flag

sub PrintResult
' pretty printer
def DiffSquares, DiffCubes: int
def it1$, it2$: string
it1$ = ltrim$(str$(it1))
it2$ = ltrim$(str$(it2))
DiffSquares = it2^2 - it1^2
DiffCubes = it2^3 - it1^3
print it2$ + "^2 - " + it1$ + "^2 = ",
print Diffsquares, "(",
print ltrim$(str$(exp(log(DiffSquares)/3))),
print "^3)"
print it2$ + "^3 - " + it1$ + "^3 = ",
print it2^3 - it1^3, "(",
print ltrim$(str$(sqrt(DiffCubes))),
print "^2)"
return