# 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 valuedef 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| > 77def main(): from itertools import count try: for x in count(2): candidate(x) candidate(-x) except KeyboardInterrupt: print "last number considered:", xmain()