There is a famous problem called camels and sons , where an old man owns camels that he wishes to be shared by his three sons after his death as follows: for the eldest son, for the second, and for the youngest.
Since is not divisible by either or the three sons consult a wise man, who proposes to lend them an extra camel. Now the eldest son can get his share of camels, the second and the youngest for a total of camels. The extra camel can then be returned to the wise man.
Suppose now that the father has camels and wants to divide the herd as follows: for the eldest son, for the second, and for the youngest. For which of the following values of can the three sons apply the same borrowing strategy to ensure that the new herd will be divided fairly and that every borrowed camel will be returned to the wise man?
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Relevant wiki: Number Base - Converting to Different Bases
We want the sharing of the herd to be ( N + b ) × ( 2 1 + 4 1 + 5 1 ) = N where b is the number of borrowed camels. Hence, b = 1 9 N and since we can only borrow whole camels ( b ∈ N ) then 1 9 ∣ N , so N = 9 5 .