Cubes and NinePro Problems > Math > Logic > Proofs
Cubes and Nine
Prove that all perfect cubes are either a multiple of 9, one more than a multiple of 9, or one less than a multiple of 9.
SolutionIn order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.
Prove that there is no two digit number which is equal to the product of its digits.
There are infinitely many angles θ between 0º and 90º for which both sin θ and cos θ are rational numbers. Prove this statement.
Hint: Here are some examples:
Four consecutive integers are multiplied together. Determine, with proof, which digits could be in the ones place of the resulting product.
Prove that all perfect squares are either a multiple of 4, or one more than a multiple of 4.
We've been providing free educational games and resources since 2002.
Would you consider a donation of any size to help us continue providing great content for students of all ages?