- #1
Entropee
Gold Member
- 134
- 0
Homework Statement
Theorem: the numbers in the set {99, 999, 9999, ... } cannot be written as two squared integers, but at least one can be expressed as the sum of 3 squared integers.
Homework Equations
Well there are a lot of examples but let's go with 32 + 32 + 92 = 99
We may have to use Euclid's division algorithm as well.
The Attempt at a Solution
If we call the first part P and the second part Q then we can assume [itex]\neg[/itex]P [itex]\vee[/itex] [itex]\neg[/itex]Q, and try to show a contradiction here.