If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?
$40$ can be written as $7^2 - 3^2.$ Which other numbers can be written as the difference of squares of odd numbers?
Which numbers cannot be written as the sum of two or more consecutive numbers?
Can you work through these direct proofs, using our interactive proof sorters?
Here are a few questions taken from the Test of Mathematics for University Admission (or TMUA).
These proofs are wrong. Can you see why?
These secondary problems have not yet been solved. Can you be the first?