15-07-2022
Mathematics

contestada

m and n are both prime numbers. Find the values of m and n so that 2704× m/n is a perfect cube.

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15-07-2022

Since 2704 = 2⁴ × 13², we need [tex]m = 13[/tex] and [tex]n=2[/tex], since this gives

[tex]\dfrac{2704m}n = \dfrac{2^4 \times 13^2 \times 13}2 = 2^3 \times 13^3 = 26^3[/tex]

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