Question

设一组正整数（a,b,c）,满足a!=4*b!+10*c!.求满足条件的组

Answer 1

显然：a > b,a > c

1.当 b = c 时,则 a!/ b!= 14,得 a = 14,b = c = 13.

2.当 b a = 4,b = 1,c = 2.ii) 无解.

3.当 b>c 时,(c+1) * ...* a = 10 + 4 * (c+1) * ...* b,

所以 10/（（c+1)*...*b ）必须是整数,所以

i) b = 2,c = 1,无解

ii) b = 5,c = 4,==> a = 6,b = 5,c = 4.

iii) b = 10,c = 9,无解.

你找出的解 只漏掉 一组：a = 14,b = c = 13.