# Solve original equation for y
# x + y - x*y = 79
#     y - x*y = 79 - x
#   y * (1-x) = 79 - x
#           y = (79-x) / (1-x)

# Find the value for y using integer math
# then check whether this gives the exact value
def candidate(x):
    y = (79-x) / (1-x)
    z = x + y - (x*y)
    if y != 0 and z == 79: print x, y

# Starting at x=2, try x and -x as candidates
# Zero is ruled out by the problem statement, and
# 1 causes division by zero so it can't be a valid 'x' either
# just keep going until interrupted, though there don't seem to be any
# integer solutions for |x| > 77
def main():
    from itertools import count
    try:
        for x in count(2):
            candidate(x)
            candidate(-x)
    except KeyboardInterrupt:
        print "last number considered:", x

main()