1. ## Counterexample

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

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

4. Originally Posted by lm6485
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.

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

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