MAT246H1 Lecture Notes - Square Root, Additive Identity, Triangle Inequality
Document Summary
Bezout"s identity: let a and b be integers, not both zero, and . Then there exist integers x and y such that: is multiplicative inverse of , , that is. If k=-2, the minimum solution is 233-2 105=23. Theorem: two simultaneous congruences are only solvable when. The solution is unique module if and are relatively primes. Since , 8-2=6 is divisible by 3, is solvable. From ex3, the general solution for is n=20+36k. Since , 20-12=8 is divisible by 4, is solvable. Thus, the general solution to the first five equations is . Since , 1-0=1 is divisible by 1, is solvable. Since , 3-7=-4 is divisible by 1, is solvable. Since , 4-40=-36 is divisible by 1, is solvable. Step1: suppose there exist integers s and t satisfying , then. Since , 7-1=6 is divisible by 3, is solvable. Suppose there exist integers s and t satisfying , then.
