book Maths Puzzle Numerical Ability

Let p be prime. Prove that...

(1 + p)^(p^(n - 1)) = 1(mod p^n) for all n = 1, 2, 3,...

Would using the Binomial Thm help? What about applying the Chinese Remainder Thm?

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book Other Question

Suppose you invest $12,000 in two funds paying 10.5% and 13% simple interest. The total annual interest is $1447.50. How much is invested in each fund? -3x > 0 and 3x -4<11
can anyone solve this