Thread: Counterexample

Find a counterexample to the statement that every positive integer can be written as the sum of the squares of three integers.

I would look fairly low. Just start at zero and work your way up.

I am not sure how to go about this.

Originally Posted by lm6485

I am not sure how to go about this.

Follow Ackbeet's advice; try to write 1 as the sum of three squares; then try to write 2 as the sum of three squares; ... and if you get stuck say where you got stuck. The smallest positive integer not expressible as the sum of three squares is less than 10.