Problem: A classical type of practise problems for the Chinese Remainder Theorem are word problems like this: A farmer’s wife is bringing eggs to market. If she divides them into groups of three, she has one left over. If she divides them into groups of five, she also has one left over. If she divides them into groups of seven, she has four left over. And if she divides them into groups of eleven, she has three left over. How many eggs does she have? Solve this problem by repeated application of the Chinese Remainder Theorem. You must explain how the solution is computed. You may assume that there are fewer than one thousand eggs.
Problem: A classical type of practise problems for the Chinese Remainder Theorem are word problems like this:
A farmer’s wife is bringing eggs to market. If she divides them into groups of three, she has one left over. If she divides them into groups of five, she also has one left over. If she divides them into groups of seven, she has four left over. And if she divides them into groups of eleven, she has three left over. How many eggs does she have?
Solve this problem by repeated application of the Chinese Remainder Theorem. You must explain how the solution is computed. You may assume that there are fewer than one thousand eggs.
In this question, we have first formed the equations, and then, using the Chinese Remainder Theorem, we have to solve the question.
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