(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

i'm sure everyone has seen this:

Solve the following ancient Indian problem: If eggs are removed from a basket 2, 3, 4,

5, and 6 at a time, there remain, respectively, 1, 2, 3, 4, and 5 eggs. But if the eggs are

removed 7 at a time, no eggs remain. What is the least number of eggs that could have

been in the basket?

2. Relevant equations

x=1%2

x=2%3

x=3%4 implies %2 (dropped)

x=4%5

x=5%6 impies %2,3 (dropped)

x=0%7

this leaves just four equations.

3. The attempt at a solution

x=1%2

x=2k+1

x=2%3

2k+1=2%3

2k=1%3

k=2%3

k=3p+2

and x=2k+1 so x= 2(3p+2)+1 = 6p+5

x=4%5

6p+5=4%5

6p=4%5

p=4%5

p=5j+4

and x=6p+5 so x=6(5j+4)=5 = 30j+29

30j+29

x=0%7

30j+29=0%7

30j=6%7

j=3%7

j=7r+3

and x=30j+29 so x=30(7r+3)+29=210r+119

so x=119%210 = 119.

how does this look? feedback appreciated.

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# Homework Help: Number Theory Problem

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