[Solved] CENG223 Take Home Exam 3

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Use Fermat’s Little Theorem theorem the find (222 + 444 + 666 + 880 + 10110) mod 11 ≡ ?

Note: Fermat’s Little Theorem is provided in our book (Kenneth H. Rosen, Discrete Mathematics and Its Applications), and it is a prerequisite for this question. This means that your solution have to use Fermat’s Little Theorem.

Question 2

Find gcd(5n + 3,7n + 4) and while doing that, show the steps of Euclid’s algorithm clearly.

Question 3

Let x be a prime number,

If m2 = n2 + kx where m, n, and k are integer numbers.

Show that x|(m + n) or x|(m n).

Question 4

Show that for all n such that n ≥ 1 the following is true:

(1)

Note: You have to use mathematical induction to prove that.

1

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[Solved] CENG223 Take Home Exam 3
30 $