1-4 summary - A summary of the maths you’ve learnt from...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: A summary of the maths you’ve learnt from Week 1 to Week 4 Written by: Vicky Mak (Burwood) [email protected] August, 2008 1 The maths we’ve learnt so far 1. Do you know how to solve ax + by = gcd(a, b)? The Extended Euclidean Algorithm 2. What can say about a and b if you can find x, y integers such that ax + by = 1? This means that gcd(a, b) = 1, that is, a and b are coprime. 2 The maths we’ve learnt so far 3. Do you know how to find the inverse of a( mod n) for a, n co-prime? Easy, solve as + nt = 1, then a−1 ≡ s( mod n). 4. How about solving ax ≡ c ( mod n)? Read Modular Not hard either, but there are 3 cases. Airthmetic slides I put on DSO. 3 The maths we’ve learnt so far 5. You need to know the Chinese Remainder Theorem. See Week 3 Lecture Slides and the additional examples inserted within the powerpoint slides. You need to know how to state the general case and of course how to use it for solving 2 simultaneous congruences. 6. The Fermat’s Little Theorem A must know! If p is prime and that p does not divide a, then ap−1 ≡ 1( mod p). 4 The maths we’ve learnt so far 7. Euler’s Theorem. Also a must know. If gcd(a, n) = 1, then aφ(n) ≡ 1( mod n), for φ(n) the number of numbers from 1 to n − 1 that are co-prime to n. 6. Primitive Roots and Square Root Modulo n What are these? See Lecture slides from Week 4. 5 ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online