1, 5, 2, and 3

(1,5,2,3)(1,5,2,3) are 4 distinct positive integers such that the sum of 2 of them equals the product of the other 2, and vice versa, i.e. the sum of these 2 other numbers equals the product of the 2 numbers initially mentioned: 1+5=2×3,2+3=1×5.1+5=2\times 3, \quad 2+3=1\times 5. Generally spoken, a+b=c×d,c+d=a×b.a+b=c\times d, \quad c+d=a\times b. Determine the number of un-ordered quadruplets (a,b,c,d)(a,b,c,d) other than (1,5,2,3)(1,5,2,3) that satisfy this condition.

×

Problem Loading...

Note Loading...

Set Loading...