5. (From problem 7.8 on Eves p. 242; also Burton, p. 231, problem 17.) Find the

Question

5. (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 thetr 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 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 You tell me now the numerical measure of a heap of plantains." so as to have no remainder

Explanation / Answer

Here as we can say that there are 63 heaps of plantain fruits and combined with 7 more fruits and can be distributed in 23 travelers.

Let say there X fruits in one heap of mountain so 63X + 7 will be the total number of fruits. which is full divisor of 23.

63X + 7 = 23k

(69 - 6)X + 7 = 23k

69X - 6X + 7 = 23k

k = 3 X - (6X -7)/23

so for X = 5; 6X -7 = 23 so it would be a complete divisor

so X would be 5m + 23 where m would be 1,2,3,...

so miniumum such number is 5..

The numerical value of each heap of plantain fruits is 5.

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