Problem of the Month


October 1999

An Infinite Number of Angles

Show there exists an infinite number of angles between 0 and p/2 whose sine and cosine are both rational.

Hint: Consider integer solutions to x2+y2=z2 (known as Pythagorean triples).

 


 

November 1999

Find the Smallest Natural Number

Part 1. Find the smallest natural number that can be expressed as the sum of the squares of two distinct natural numbers in two different ways. (That would entail altogether, four distinct natural numbers that are squared.)

Part 2. Find the smallest natural number that can be expressed as the sum of the squares of two, not necessarily distinct, natural numbers in two different ways.


Hit Counter

Home ]                 Up ] Next ]