The difference between the squares of two even positive integers that are less than 100 apart equals 10!(factorial). What are the two integers? Thank you for any help.
I don't know how to solve such a problem mathematically. I will leave it to one of the mathematicians to shed some light on it. However, it is a trivial matter to write a very short computer code to find the solution(s) almost intantaneously
a=20000; b=1;c= (a+b)^2 - a^2; if(c==10!, goto4, goto5);printc, a, b; a++;if(a<25000, goto2, 0);a=20000;b++;if(b<100, goto2, discard=0;
As it turns out, you have more than one solution! In fact, there are 4 sets of solutions as follows:
(a + b)^2 - a^2 = 10!
a = 1,814,400/b - b/2
a b
22640 80 =(22,640 + 80)^2 - 22,640^2 =10!
21558 84 =(21,558 + 84)^2 - 21,558^2 =10!
20115 90 =(20,115 + 90)^2 - 20,115^2 =10!
18852 96 =(18,852 + 96)^2 - 18,852^2 =10!