Problem
COM-B1-M06-P004 Residue of a Sum
#4
★☆☆☆☆ Level 1 of 5
A number on the board may be changed by adding \(6\) or subtracting \(9\). Starting from \(5\), can one obtain \(100\)?
The changes are multiples of \(3\).
The residue modulo \(3\) is preserved. \(5\equiv2\pmod3\), while \(100\equiv1\pmod3\). Therefore \(100\) cannot be obtained.
First modular invariant.