A band of 23 weary travelers entered a lush forest where they found 63 piles each of containing the same number of plantains and a remaining pile containing 7 plantains. They divide the plantains equally among them. How many plantains were in each of the 63 piles?
A band of 23 weary travelers entered a lush forest where they found 63 piles each of containing the same number of plantains and a remaining pile containing 7 plantains. They divide the plantains equally among them. How many plantains were in each of the 63 piles?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A band of 23 weary travelers entered a lush forest where they found 63 piles each of containing the same number of plantains and a remaining pile containing 7 plantains. They divide the plantains equally among them. How many plantains were in each of the 63 piles?
Expert Solution
Step 1
The Diophantine equation is very important in number theory. It contains two variables and one equation. The solution we seek is an integer solution. Euclid's algorithm is followed to solve a Diophantine equation. First, we determine the greatest common divisor of the two integer coefficients of the variable. Then, we follow extended Euclid's algorithm to find Bezout's coefficient. Then, it will be one of the basic solutions of the equation.
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