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MATH / Let i be the smallest positive integer such that 3^iequiv 5pmod 7. Let j be the smallest positive integer such that 5^jequiv 3pmod 7. What is the remainder when ij is divided by 6?

Problem

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problem

Let ii be the smallest positive integer such that $3^i\equiv 5\pmod 7.$ Let jj be the smallest positive integer such that $5^j\equiv 3\pmod 7.$ What is the remainder when ijij is divided by $6?$
Plain-text mathematical notation (without MathML)
Let i be the smallest positive integer such that $3^i\equiv 5\pmod 7.$ Let j be the smallest positive integer such that $5^j\equiv 3\pmod 7.$ What is the remainder when ij is divided by $6?$
Original LaTeX notation
Let $i$ be the smallest positive integer such that $3^i\equiv 5\pmod 7.$ Let $j$ be the smallest positive integer such that $5^j\equiv 3\pmod 7.$ What is the remainder when $ij$ is divided by $6?$

level

Level 3

type

Number Theory

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Source and history

task_id
0743f05d-eac7-5fd7-a648-e2fda7338096
task_key
number~5ftheory--test--0743f05d-eac7-5fd7-a648-e2fda7338096
task_revision_id
1
config / split
number_theory / test

Official source

initial import