Verified answer

We must have a² − b² = kp

⇒ (a + b) (a − b) = kp

⇒ either a − b = 0 or a + b is a multiple of p

when a = b; number of matrices is p

and when a + b = multiple of p ⇒ a, b has p − 1

∴ Total number of matrices = p + p − 1

= 2p − 1

Hope this helps!

in case you ever took precalculus or another math class which covers properties of purposes, you straightforward procedures to be certain the area of the function. between the red flags to look out for is once you divide by using 0. on your expression, at the same time as x = 3, the denominator is 0. for this reason, the area is each and every kind beside 3. regrettably, the kind you attempt to plug in (x = 3) is the really kind that doesn't paintings in this function. to be certain this favourite hand, you0 can graph this function on a TI-80 3. in case you zoom in on the point of the graph at x = 3, you'll locate there's a sparkling spot there! it quite is because, as suggested above, there in simple terms isn't a fee of the expression at x = 3. you may want to assert, properly it sounds like the reply might want to be 6, searching on the graph. this concept of what the reply "might want to be" is what limits are all about. The values of the function on the left and suitable of x = 3 all go in the route of 6 as you seize up with and closer. So we are saying the reduce as x is going to three is 6. So besides the actual undeniable truth that it is not technically the reply, 6 is your ideal decision. 0 should not be outstanding in any experience. the very ideal answer is to assert that the expression is undefined at x = 3. This project illustrates why 0/0 is termed indeterminate. in this project, 0/0 in a way equals 6. the concept 0/0 can equivalent something is totally the essence of calculus.