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1. a. For each number n from 1 to 4, compute n4 modulo 5, leaving your...

1. a. For each number n from 1 to 4, compute n4 modulo 5, leaving your answer as a number from 0 to 4.

b. Based on your answers in Problem (a), make a guess for the number np−1 (mod p) when p is any prime number and n is a number from 1 to p−1?

c. Using your conjecture from part (b), and some properties of exponents, calculate 81 000 000 (mod 11), leaving your answer as a number from 0 to 10.

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Answer #1
  • Pre-requisite is knowing about congruences and modulo and their properties . IF I have mentioned a|b that means a divides b ( which is known to you).
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