a tough diophantine equation

diophantine equation involving only positive integers, the natural numbers i do not resent there was no asian in that scene i just enjoyed the peaceful and loving interactions between blacks and whites https://www.youtube.com/watch?v=2vdF6NASMiE ... i had to think about it for twenty minutes or so ... you fill 5 gallon jug with water, pour it to 3 gallon empty jug 5 gallon jug is left with 2 gallons of water ... then you empty 3 gallon jug then you transfer the 2 gallons of water from 5 gallon jug to 3 gallon jug ... now 5 gallon jug is empty and 3 gallon jug has 2 gallons of water ... next you fill 5 gallon jug with full water then you transfer 1 gallon of water from 5 gallon jug to 3 gallon jug cuz 3 gallon jug has only 1 gallon of empty space ... so 5 gallon jug now has only 4 gallons of water ... problem solved //:-)