How do I find the sum of prime factors of $(1750 + 1225)^{1229}$?

Question

The number is: $(1750 + 1225)^{1229}$

My professor did this example in class, but I didn't really understand this. Please help.

Thanks.

Answer 1

Assuming, given the lack of clarity, that you need to find the sum of distinct prime factors (disregarding multiplicity of any given prime factor), find the prime factors of the sum $$1750 + 1225 = 2975$$

$$(1750 + 1225)^{1229} = (2975)^{1229} = (5^2 \cdot 7 \cdot 17)^{1229}= \left(5^2\right)^{1229}\cdot (7)^{1229}\cdot (17)^{1229}$$

Now you need to determine whether you need to

• sum $2\cdot 1229$ factors of 5, and $1229$ factors of $7$, and $1229$ factors of $17$

• or simply sum the distinct prime factors $5$ and $7$ and $17$: In the latter case, your sum will be $5 + 7 + 17 = 29$.

Either way, you'll have your result.