The squares of three positive integers are in arithmetic progression, and the third integer is 12 more than the first. Find the three integers.
I will give the answer courtesy of a short computer code. Cphill will give an algebraic solution:
a=1; b=13;c= b-a; if(c==12, goto4, goto6);d=2#((b^2- a^2)/2 + a^2);printd,a,b; a++;b++;if(a<1000, goto2, 0)
The number are: 2^2 , 10^2, 14^2 4, 100, 196