#----------------------------------------------------------------------- # ramanujanwhile.py #----------------------------------------------------------------------- import stdio import sys # Accept integer n as a command-line argument. Write to standard # output any integer between 1 and n that can be expressed as the # sum of two cubes in two (or more) different ways. # # Bug: If a number can be expressed as a sum of cubes in more than two # different ways, the program writes some duplicates. # Accept one command-line argument. n = int(sys.argv[1]) # For each a, b, c, d, check whether a^3 + b^3 = c^3 + d^3. a = 1 while a <= n: a3 = a*a*a if a3 > n: break # Start at a to avoid print out duplicate. b = a while b <= n: b3 = b*b*b if a3 + b3 > n: break; # Start at a + 1 to avoid printing out duplicates. c = a+1 while c <= n: c3 = c*c*c if c3 > a3 + b3: break # Start at c to avoid printing out duplicates. d = c while d <= n: d3 = d*d*d if c3 + d3 > a3 + b3: break if c3 + d3 == a3 + b3: stdio.write(str(a3+b3) + ' = ') stdio.write(str(a) + '^3 + ' + str(b) + '^3 = ') stdio.write(str(c) + '^3 + ' + str(d) + '^3') stdio.writeln() d += 1 c += 1 b += 1 a += 1 #----------------------------------------------------------------------- # python ramanujanwhile.py 2000 # 1729 = 1^3 + 12^3 = 9^3 + 10^3 # python ramanujanwhile.py # 100001729 = 1^3 + 12^3 = 9^3 + 10^3 # 4104 = 2^3 + 16^3 = 9^3 + 15^3