Question

已知m,n,p,q满足：mnpq=6(m-1)(n-1)(p-1)(q-1).

Answer 1

(1)

设m,n,p,q减1后为a,b,c,d

那么(1+1/a)(1+1/b)(1+1/c)(1+1/d) = 6

设a >= b >= c >= d那么d必须为1,否则(3/2)^4 < 6

所以(1+1/a)(1+1/b)(1+1/c) = 6 * 1/2 = 3

若c = 1那么(1+1/a)(1+1/b)=3/2 此时显然无整数解

所以c >= 2

若c = 2那么(1+1/a)(1+1/b) = 3*2/3 = 2,可知此时a = 3 ,b = 2是唯一一组解

若c >= 3那么(1+1/a)(1+1/b)(1+1/c)