Question

若正整数a.b.c.x.y.z满足ax=b+c by=c+a cz=a+b求乘积xyz可能取值个数

Answer 1

axbycz = (b+c)(a+c)(a+b) >= 8abc所以xyz >= 8设x>=y>=z若x>=2 ,y>=2 ,z>=2那么2(a+b+c) = ax+by+cz >= 2(a+b+c)所以此时给出x = y = z = 2若z = 1那么c = a+bax = b+c = a+2b =>x = 1 + 2b/aby = a+c = 2a+b =>y =...