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.
Find gcd(5n + 3,7n + 4) and while doing that, show the steps of Euclid’s algorithm clearly.
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).
Show that for all n such that n ≥ 1 the following is true:
Note: You have to use mathematical induction to prove that.