+50 Given that is a prime number, evaluate
$$1^{-1} \cdot 2^{-1} + 2^{-1} \cdot 3^{-1} + 3^{-1} \cdot 4^{-1} + \cdots + (p-2)^{-1} \cdot (p-1)^{-1} \pmod{p}.$$
+33616 I suggest you put your LaTeX in the LaTeX box - select the \(\sum \text{LaTeX}\) Icon on the menu bar of the input page.
You don't need the $$ symbols when you do this.
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+50 And this, too.
"Modulo 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 y\(\equiv{x^2}\)would consist of the points (0,0),(1,1) ,(2,4) ,(3,4) , and (4,1).
The graph of $$3x\equiv 4y-1 \pmod{35}$$ 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 $x_0+y_0$?
