Timmy has successfully shown Suzie's conjecture is incorrect
Suzie's conjecture is correct if the smallest square in the sum is 1
Step-by-step explanation:
The sum of odd numbers 1 .. n is ((n+1)/2)², a perfect square. Suzie is right about that. What Timmy has shown is that she is incorrect that the conjecture applies to <em>any</em> sum of consecutive odd numbers.
Timmy's sum of 5+7+9 is incorrect; it is 3·7 = 21. But, Timmy has the right idea. The sum of an arbitrary set of consecutive odd numbers will be the difference of two squares, but not necessarily a perfect square.
