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Prime Factorisation

For any natur...

Question

For any natural numbers ( m,n ) , prove that ( m³ + n³ + 4 ) cannot be a perfect cube .

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m

consecutive natural numbers be

n + 1, n + 2, \dots, n + m

Prove that sum of cubes of any number of consecutive natural numbers is always divisible by the sum of these numbers.

3^{n} \times 4^{m}

cannot end with the digit 0 or 5 for any natural numbers

^{'} n^{'}

^{'} m^{'}

Q. Prove that the product of four consecutive natural numbers cannot be a perfect cube.

4^{n}

cannot end with the digit zero for any natural number n .

Q. For any natural number

n, 4^{n}

cannot end with which of the following?

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