So this number is the common multiple of 2, 3, 4, 5, 6, 7, 8, 9, 10 minus 1.
The least common multiple of 2, 3, 4, 5, 6, 7, 8, 9, 10 is 2520.
Therefore, the minimum value is 25 19, 1. According to the conditions, it is divided into 2+ 1, 3+2, 4+3, 5+4, 6+5, 7+6, 8+7, 9+8, 10+9.
Then it means that if you add 1, this number can be divisible by 2, 3, 4, 5, 6, 7, 8, 9 and 10 at the same time. We are looking for the least common multiple of 2, 3, 4, 5, 6, 7, 8, 9 and 10 to be 2520.
So this number is 2520- 1=25 19.
The answer is 25 19 (the question should be accompanied by minimum conditions) ... 2, 10! - 1, 1,x = 10a+9 = 10(a+ 1)- 1
=9b+8=9(b+ 1)- 1
=8c+7=8(c+ 1)- 1
=7d+6=7(d+ 1)- 1
=6e+5=6(e+ 1)- 1
=5f+4=5(f+ 1)- 1
=4g+3=4(g+ 1)- 1
=3h+2=3(h+ 1)- 1
= 2i+ 1 = 2(I+ 1)- 1
So x+ 1 is the common multiple of 2, 3, 4, 5, 6, 7, 8, 9, 10.
x+ 1=2520n n∈N
x=2520n- 1
The minimum x is 25 19, 1. I think this is a classic and ingenious math problem ...?
Specifically, a number is divided by 10+9, 9+8, 8+7, 7+6, 6+5, 5+4, 4+3, 3+2 and 2+0. What is the number?