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Square expressions (Posted on 2017-02-18) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Ady TZIDON    
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Hints/Tips A solution | Comment 1 of 3

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

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