2. consider congruence x^2 ≡ 16 (mod 105) for integer x
a. Give one sample solution of the congruence in the range 0≤x≤104 that is different from 4 and also from 101
b. Find the number of solutions of ths congruence among integers in the range 0≤x≤104 by resorting to the Chiness Reminder Theorem
Clarification: you are not asked to list all solutions. In particular, a direct inspection of each number x such that 0≤x≤104 for satisfying congruence x2 ≡ 16 (mod 105).
3. Use mathematical induction to show that 3 divides n^3 + 2n, whenever n is a natural number.
4. Let fn denote the n-th Fibonacci number. Use mathematical inducation to show that
fn+1fn-1 - f2n = (-1)2
for all positive integers n
Euclidean algorithm is applied.