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MATH / Euler discovered that the polynomial p(n)=n²−n+41 yields prime numbers for many small positive integer values of n. What is the smallest positive integer n for which p(n) and …

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problem

Euler discovered that the polynomial p(n)=n2−n+41p(n) = n^2 - n + 41 yields prime numbers for many small positive integer values of nn. What is the smallest positive integer nn for which p(n)p(n) and p(n+1)p(n+1) share a common factor greater than 11?
Plain-text mathematical notation (without MathML)
Euler discovered that the polynomial p(n)=n²−n+41 yields prime numbers for many small positive integer values of n. What is the smallest positive integer n for which p(n) and p(n+1) share a common factor greater than 1?
Original LaTeX notation
Euler discovered that the polynomial $p(n) = n^2 - n + 41$ yields prime numbers for many small positive integer values of $n$. What is the smallest positive integer $n$ for which $p(n)$ and $p(n+1)$ share a common factor greater than $1$?

level

Level 5

type

Number Theory

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Source and history

task_id
38ed1985-ca8b-5131-806d-a6ee5658cea0
task_key
number~5ftheory--test--38ed1985-ca8b-5131-806d-a6ee5658cea0
task_revision_id
1
config / split
number_theory / test

Official source

initial import