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.
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Four consecutive integers are multiplied together. Determine, with proof, which digits could be in the ones place of the resulting product.
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:
Prove that all perfect squares are either a multiple of 4, or one more than a multiple of 4.
Prove that there is no two digit number which is equal to the product of its digits.
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