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 2017-02-20 09:20:47