# Perfect square/cube/fifth power

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Find the smallest positive integer N such that N/2 is a perfect square, N/3 is a perfect cube and N/5 is a perfect fifth power.

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INSTRUCTIONS TO OTA

1. typeset solutions

2. send solution as attachment

3. Use words to explain solutions. DO NOT RELY ONLY ON ALGEBRAIC MANIPULATIONS/ OR SYMBOLS.

Find the smallest positive integer N such that N/2 is a perfect ...

#### Solution Summary

This is a proof regarding integers, divisibility, and powers.

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