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Are there any integers $a,b$, such that:

$$a^2+4b^2 , 4a^2+b^2$$

are both perfect squares?

  • 0
    What is an imperfect square?2012-08-20
  • 7
    As usual: what have you tried? Is this homework? What is the motivation?2012-08-20
  • 1
    @celtschk "Perfect" squares emphasizes that they are squares of integers, as every positive real number is the square of some real number.2012-08-20
  • 1
    @Old John i have possible solution , http://store2.up-00.com/Aug12/HNY76345.jpg2012-08-20
  • 0
    @MohammedAl-mubark: You should mention the trivial solutions.2012-08-20
  • 0
    Use Euclid's formula (see [here](http://en.wikipedia.org/wiki/Pythagorean_triple))2012-08-20
  • 0
    Tested for a,b = 1 to 1 million. No solutions.2012-08-20

2 Answers 2