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

The perimeter of a rectangular floor is 42 feet, and the area is 108 square feet. Find the length of the floor. solve the linear system...if the system is inconsistent or dependent, so state

3x-2y = 0
9x-8y= 7