Monday, June 17, 2019

elementary number theory - Diophantine equation

There were 63 equal piles of plantain fruit put together and 7 single fruits. They were divided evenly among 23 travelers. What is the number in each pile. Consider the Diophantine equation 63x+7=23y



So I found one solution: -7= 6(-28)+23(7)
so then I plugged it into the formula to find all solutions and got
x=-28-23t and y=-28-6t



so then I got t<-1.2 and t<-4.7 but this range is huge.. where did I go wrong?

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