(From problem 7.8 on Eves p. 242; also Burton, p. 231, problem 17.) Find the sma
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Question
(From problem 7.8 on Eves p. 242; also Burton, p. 231, problem 17.) Find the smallest permissible answer to the following indeterminate problem of Mähavira (ca 850 AD). "Into the bright and refreshing outskirts of a forest, which were full of numerous trees with their branches bent down with the weight of flowers and fuits, trees such as jambu trees, lime trees, plantains, areca palms,jack trees, date palms, hintala trees, palmyras, punnaga trees, and mango trees outskirts, the various quarters whereof were filled with the many sounds of crowds of parrots and cuckoos found near springs containing lotuses with bees roaming about them into such forest outskirts a number of weary travelers entered with joy. There were 63 numerically equal heaps of plantain fruits put together and combined with 7 more of those same fruits, and these were equally distributed among 23 travelers so as to have no remainder You tell me now the numerical measure of a heap of plantains.' . An integer n is squarefree if n is not divisible by any squares, that is, every prime that appears in the factoring of n ars just once. The first few examples are 2, 3, 5, 6, 7, 10, 11, 13,..Explanation / Answer
There are 63 numerically equal heaps of plaintain fruits. These fruits were put together and combined with 7 more of the same fruits. These were equally distributed among 23 travellers so that there is no remainder.
(63x + 7)/23 = whole number
Consider the value of x to be 5,
= 63(5) + 7
= 315 + 7
= 322
When this number is divided by 23, we will get 14 with no remainders.
Therefore, the numerical measure of heap of a plantains is 5.
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