What is the remainder when we divide $5^{70}+7^{70}$ by 74?

Answer:

Concept Used:

If n is odd then, an + bn is divisible by (a + b)

Calculation:

Here given,

5⁷⁰ + 7⁷⁰

⇒ 25³⁵ + 49³⁵

Here n = 35, which is an odd number.

⇒ aⁿ + bⁿ is divisible by (a + b)

⇒ 2535 + 49³⁵ is divisible by (25 + 49) = 74

⇒ (5²)³⁵ + (7²)³⁵ is divisible by 74

⇒ 5⁷⁰ + 7⁷⁰ is divisible by 74

So, we can say 5⁷⁰ + 7⁷⁰ is completely divisibly by 74.

So, the remainder is 0.

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