NUMBER THEORY.

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Presentation transcript:

NUMBER THEORY

Prime Numbers Prime number: only divisible by 1 and itself. Fundamental Theorem of Arithmetic How many primes are there?

How to find primes from math import sqrt topnum = int(raw_input("Enter the highest number to check: ")) startnum = 3 print 2 print 3 while startnum < topnum: for a in range(3,int(sqrt(startnum+1)),2): if startnum % a ==0: break; else: print startnum startnum = startnum + 2

Divisibility p | q definition. Factoring a number… gcd lcm modular arithmetic Applications: Change Last digit Encryption Calendar computations

Congruences Modular equations. Solving congruences… Diophantine equations

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