Due Date Is Over
Due Date: 05-11-2024
DIVISIBILITY THEORY AND CANONICAL DECOMPOSITI
1 State divisible algorithm
2 State pigeon hole principle
3 State principle of inclusion and exclusion
6 Express (10110)2 in base 10 and express (1076)10 in base two
7 Express (1776)8 in base 10 and express (676)10 as octagonal
8 Express (1976)16 in base 10 and express (2076)10 as hexadecimal
10 Express (12,15,21) as a linear combination of 12, 15, and 21
12 Use canonical decomposition to Evaluate the GCD of 168 and 180
13 Use canonical decomposition to evaluate LCM of 1050 and 2574
14 Find the canonical decomposition of 2520
15 Find the prime factorization of 420, 135, 1925
16 Using recursion evaluate (252, 360)
17 Using recursion evaluate [24,28,36,40]
18 Using recursion evaluate (18,30,60,75,132)
19 Find the GCD (414,662) using Euclidean algorithm
20 Find the LCM (120.500)
21 State and Prove Euclidean algorithm
22 Find the number of positive integers ≤ 3000 divisible by 3, 5 or 7
23 Prove that the GCD of two positive integers a and b is a linear
combination of a and b
24 Find the number of positive integers in the range 1976 through 3776
that are divisible by 13 and not divisible by 17
25 Find the number of integers from 1 to 250 that are divisible by anyof
the integers 2,3,5,7
26 Prove by induction that 2ð‘›3 + 3ð‘›2 + ð‘› is divisible by 6 for all
integers 𑛠≥ 0
27 State and prove Fundamental Theorem of Arithmetic.
28 Prove that every integer 𑛠≥ 2 has a prime factor.
29 Use Euclidean algorithm to find the GCD of (1819, 3587). Also
express the GCD as a linear combination of the given numbers
