Homework Sourseevery sixdigit number of the form abcabc is divisible by 11
every six-digit number of the form abcabc is divisible by 11.
true or false. provide justification.
every six-digit number of the form abcabc is divisible by 11.
true or false. provide justification.
every six-digit number of the form abcabc is divisible by 11.
true or false. provide justification.
Solution
Suppose that a=1, b=2, c=3 so that abc=123. Then
1231000=123000
=> 1231=123
=> 1231000+1231=123000+123=123123
=> 1231001=123123.
In other words
abcabc=abc1001.
It\'s a little fact that 71113=1001. And multiplying any three digit number by 1001 will give a number of the form abcabc.
