What are the positive integers
k and m,
if both k^2 + 4m and m^2 + 5k are squares of integers?
P&p solution to list all the possible couples.
Substitution: Let m=k+1, then a^2 = (k + 2)^2, b^2 = k^2 + 7k + 1}
k=1, m=2:
a^2=3^2 = 1^2+4*2
b^2 = 3^2 = 2^2+5*1
k=8, m=9:
a^2 = 10^2 = 8^2 + 4*9,
b^2 =11^2 = 9^2 + 5*8.
And that is all.
Edited on February 20, 2017, 9:44 am

Posted by broll
on 20170220 09:20:47 