Quadratic equations - UCLA Department of Mathematics
... Ancient problem: ancient and modern solution 1. Let’s try to follow the reasoning in ancient Egypt to solve the following problem: Find two numbers whose sum is 20 and whose product is 96. The Egyptians argued as follows: if the numbers would be equal, each of them would be 10 and the product would ...
... Ancient problem: ancient and modern solution 1. Let’s try to follow the reasoning in ancient Egypt to solve the following problem: Find two numbers whose sum is 20 and whose product is 96. The Egyptians argued as follows: if the numbers would be equal, each of them would be 10 and the product would ...
Fermat`s Little Theorem
... This process can be continued indefinitely to prove the result. (Technically, the result ap ≡ a mod p is found by induction on a.) An important use of this result is the following: Theorem: If a is not divisible by p, the inverse of a mod p is ap−2 . This is clearly true since 1 ≡ ap−1 ≡ a · ap−2 mo ...
... This process can be continued indefinitely to prove the result. (Technically, the result ap ≡ a mod p is found by induction on a.) An important use of this result is the following: Theorem: If a is not divisible by p, the inverse of a mod p is ap−2 . This is clearly true since 1 ≡ ap−1 ≡ a · ap−2 mo ...
open ppt file
... Solve the quadratic inequality –x2 + 5x + 3 > 0 . Answer: This inequality holds for those values of x for which the graph of f (x) is at or above the x axis. This happens for x between the two x intercepts, including the intercepts. Thus, the solution set for the quadratic inequality is – 0.5414 < x ...
... Solve the quadratic inequality –x2 + 5x + 3 > 0 . Answer: This inequality holds for those values of x for which the graph of f (x) is at or above the x axis. This happens for x between the two x intercepts, including the intercepts. Thus, the solution set for the quadratic inequality is – 0.5414 < x ...
Pythagoras Pythagoras A right triangle, such as shown in the figure
... • For security purposes, the integers p and q should be chosen at random, and should be of similar bit-length. Prime integers can be efficiently found using a primality test. (2) Compute n = pq. • n is used as the modulus for both the public and private keys (3) Compute φ(n) = (p − 1)(q − 1). (4) C ...
... • For security purposes, the integers p and q should be chosen at random, and should be of similar bit-length. Prime integers can be efficiently found using a primality test. (2) Compute n = pq. • n is used as the modulus for both the public and private keys (3) Compute φ(n) = (p − 1)(q − 1). (4) C ...
