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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.

 May 21, 2019
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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!

 May 21, 2019

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