Go Pro!

Problems > The Maine Page > 2002

Complex Proof

Let x and y be real integers such that x > y > 0. If a + bi is the square of x + yi, prove that a and b are the legs in a pythagorean triple -- that is, if a and b are whole number lengths of the legs in a right triangle, the hypotenuse will also be a whole number. (i is the imaginary unit.)

For 2 bonus points, specify less restrictive conditions on the integers x and y for which the above statement is still true.

View the solution
Toothpick Polygon
Thanks, Soroban

Understanding Coronavirus Spread

A Question and Answer session with Professor Puzzler about the math behind infection spread.

Blogs on This Site

Reviews and book lists - books we love!
The site administrator fields questions from visitors.
Like us on Facebook to get updates about new resources
Pro Membership