Verify that 133 divides 11n+2 + 122n+1 for every natural number n.

Question

Verify that 133 divides 11ⁿ⁺² + 12²ⁿ⁺¹ for every natural number n.

08 Feb 2021

Answer :

Word Count : 310

To verify whether 133 divides the expression 11n+2 + 122n+1 for every natural number n, we need to show that the expression is divisible by 133, which means that it yields an integer result.

Let's rewrite the expression as follows:

11n+2 + 122n+1 = 11n * 11^2 + 2 * 11^2 + 122n * 11 + 122

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