Proving that the square of every odd integer takes a specific algebraic form.
Show that the square of every odd integer is of the form: 8k+1.
Finding the remainder of a number using Fermat's Theorem.
Find the remainder of 2^1000 divided by 7 by using Fermat's Theorem.
By brute force, find a multiplicative inverse to 31 mod 100. Is there only one, or can you find more??
Application of Mathematical Induction It is an application of Mathematical Induction in proving the relations of Fibonacci Numbers. To prove: F 2n+1 - Fn Fn+2 = (-1) n for n > or, = 3.
Find the probability when two fair dice are rolled the point is 11,given that one of the die is less than 5. Please don't attach files because I'm having a hard time opening some of them.Just briefly explain with answer.
Combinatorial and Computational Number Theory Fermat’s Little Theorem Greatest Common Divisor
See attached file for full problem description. (a) Prove that if g.c.d.(n,p) = 1,then p divides n^(p-1) –1. (b) Prove that if 3 is not a divisor of n, then 3 divides ...continues
Linear Congruences Set of Mutually Incongruent Solutions
Find a complete set of mutually incongruent solutions of each of the following . (a) 7x is congruent to 5 (mod 11) (b) 8x is congruent to 10 (mod 30) (c) 9x is congruent to 12 (mod 15)
Linear Congruences - The Chinese Remainder Theorem
Find all solutions of each of the systems of congruences:- (a) x is congruent to 1 (mod 2) (d) 4x is congruent to 2 (mod 6) x is congruent to 2 (mod 3) ...continues
Linear Congruences - Application of Chinese Remainder Theorem
Find the least positive integer that yields the remainders 1,3 and 5 when divided by 5,7 and 9 respectively.
The Fermat numbers are numbers of the form 2 ^2n + 1 = Φn . Prove that if n < m , then Φn │Φm – 2. The Fermat numbers are numbers of the form 2 ^2n + 1 = (Phi)n . Prove that if n < m , then (Phi)n │(Phi)m – 2.
