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OlympiadBench / 1833 / Find all pairs (p,q) of prime numbers with p>q for which the number

Problem

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

answer type

Tuple

is multiple answer

false

language

English

question

Find all pairs

(p, q)

of prime numbers with

p>q

for which the number

\frac{(p+q)^{p+q}(p-q)^{p-q}-1}{(p+q)^{p-q}(p-q)^{p+q}-1}

is an integer.

Plain-text mathematical notation (without MathML)

Find all pairs (p,q) of prime numbers with p>q for which the number

((p+q)^(p+q)(p−q)^(p−q)−1)/((p+q)^(p−q)(p−q)^(p+q)−1)

is an integer.

Original LaTeX notation

Find all pairs $(p, q)$ of prime numbers with $p>q$ for which the number

$$
\frac{(p+q)^{p+q}(p-q)^{p-q}-1}{(p+q)^{p-q}(p-q)^{p+q}-1}
$$

is an integer.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1833
task_id: 608e69d5-6748-5e56-a98e-02b8e7e68df2
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1833
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import