Create a dictionary D where the keys are all natural numbers @@0@@ from 1 to 100, and the values are the squares @@1@@ of these numbers

Create a list @@0@@ of the first 100 odd numbers

Determine the partial sums @@0@@

List all keys @@0@@ of D, for which there is a partial sum @@1@@

Can you give a general mathematical statement of your finding, and proof that it is correct, even beyond @@0@@?