Seudónimo Seudónimo
  • 16-04-2020
  • Mathematics
contestada

Find the sum of the distinct prime factors of $5^5 - 5^3$.

Respuesta :

Bracool
Bracool Bracool
  • 11-07-2021

Answer:

10

Step-by-step explanation:

The largest power of $5$ that divides both terms is $5^3$. We factor out $5^3$ as follows: \begin{align*}

5^5 - 5^3 &= 5^3 \cdot 5^2 - 5^3 \cdot 1 \\

&= 5^3(5^2 - 1)

\end{align*}$5^2 - 1 = 24$, which factors as $2^3 \cdot 3$. Thus, the prime factorization is ${2^3 \cdot 3 \cdot 5^3}$, and the sum of the prime factors is $2+3+5 = \boxed{10}$.

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