Problems(1)
The 2m numbers
1\cdot 2, 2\cdot 3, 3\cdot 4,\hdots,2m(2m+1)
are written on a blackboard, where m≥2 is an integer. A move consists of choosing three numbers a,b,c, erasing them from the board and writing the single number
ab+bc+caabc
After m−1 such moves, only two numbers will remain on the blackboard. Supposing one of these is 34, show that the other is larger than 4. algebra