Number Theory

Prime Factorization and Divisors

Perfect Squares, Cubes and Powers

         

Which of the following is NOT a perfect square number?

If 270x270x is a perfect square, what is the smallest possible integer value of x?x?

Divide 297297 by the smallest possible positive integer aa so that the result is the square of a positive integer bb. What is a+ba+b?

Find the smallest positive integer c c that satisfies

360a=1500b=c2, 360a = 1500b = c^2,

where aa and bb are positive integers.

Find the largest 4-digit positive integer which is a perfect power of 2.

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