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MATH / Given that p≥7 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}.

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Given that p≥7p\ge 7 is a prime number, evaluate $$1^{-1} \cdot 2^{-1} + 2^{-1} \cdot 3^{-1} + 3^{-1} \cdot 4^{-1} + \cdots + (p-2)^{-1} \cdot (p-1)^{-1} \pmod{p}.$$
Plain-text mathematical notation (without MathML)
Given that p≥7 is a prime number, evaluate $$1^{-1} \cdot 2^{-1} + 2^{-1} \cdot 3^{-1} + 3^{-1} \cdot 4^{-1} + \cdots + (p-2)^{-1} \cdot (p-1)^{-1} \pmod{p}.$$
Original LaTeX notation
Given that $p\ge 7$ is a prime number, evaluate $$1^{-1} \cdot 2^{-1} + 2^{-1} \cdot 3^{-1} + 3^{-1} \cdot 4^{-1} + \cdots + (p-2)^{-1} \cdot (p-1)^{-1} \pmod{p}.$$

level

Level 5

type

Number Theory

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Source and history

task_id
10f104bd-3339-5eca-9ce0-b28d834bf52c
task_key
number~5ftheory--test--10f104bd-3339-5eca-9ce0-b28d834bf52c
task_revision_id
1
config / split
number_theory / test

Official source

initial import