+50
1)Given that is a prime number, evaluate
\(1^{-1} \cdot 2^{-1} + 2^{-1} \cdot 3^{-1} + 3^{-1} \cdot 4^{-1} + \cdots + (p-2)^{-1} \cdot (p-1)^{-1} \pmod{p}.\)
+50 "Modulo m graph paper" consists of a grid of m^2 points, representing all pairs of integer residues (x,y) where 0=<x=<m. To graph a congruence on modulo m graph paper, we mark every point (x,y) that satisfies the congruence. For example, a graph of ywould consist of the points (0,0),(1,1) ,(2,4) ,(3,4) , and (4,1).
The graph of has a single x-intercept $(x_0,0)$ and a single y-intercept $(0,y_0)$, where $0\le x_0,y_0<35$.
What is the value of $x_0+y_0$?
Sorry, too lazy for LaTeX now,
+14923 Hello thisismyname!
1^(-1) * 2^(-1) + 3^(-1) * 4^(-1) + 4^(-1) * 5^(-1) + 5^(-1) * 6^(-1) + 6^(-1) * 7^(-1) +...+ (p-2)^(-1) * (p-1)^(-1)
= 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 +.....+ (p-2)^(-1) * (p-1)^(-1)
This is the sum of the reciprocals of the square numbers p k to p.
Unfortunately, I know only the formula for the limit of all.
.
A rectangle number or pronische number p, is a number that is the product of two successive natural numbers.
The first square-wave numbers p are 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110
The sum of the reciprocals of all square numbers k = \(\frac{1}{p} \) is 1.
\(\sum\limits_{k=1}^{\infty }\frac{1}{k^{2}+k } =1\)
For my English I apologize.
Greeting asinus :- ) 
!
