Equation Solving

Find all real number(s) $x$ such that $2^x+3^x+6^x-4^x-9^x=1 $ $$$$ This problem can be solved by transforming the equation where it can be written as sum of squares of number equals zero. From there the result will follow. See the video below for the explanation. $$$$

Sophie Germain Identity

Here is a problem of primality testing of a number. As you can see a direct computation will not yield an effective result and will take a much longer time! So, the question arises how to solve the problem in the right way. Here comes the roll of simple and elegant identity known as Sophie Germain Identity. Watch the video below for the solution

For solution of the problem above watch the video below.