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Omni-MATH / Determine all such pairs pf positive integers (a,b) such that a+b+(gcd(a,b))²=lcm(a,b)=2⋅lcm(a−1,b), where lcm(a,b) denotes the smallest common multiple, and gcd(a,b) denotes the g…

Problem

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problem

Determine all such pairs pf positive integers (a,b)(a, b) such that a+b+(gcd(a,b))2=lcm(a,b)=2⋅lcm(a−1,b)a + b + (gcd (a, b))^ 2 = lcm (a, b) = 2 \cdot lcm(a -1, b), where lcm(a,b)lcm (a, b) denotes the smallest common multiple, and gcd(a,b)gcd (a, b) denotes the greatest common divisor of numbers a,ba, b.
Plain-text mathematical notation (without MathML)
Determine all such pairs pf  positive integers (a,b) such that  a+b+(gcd(a,b))²=lcm(a,b)=2⋅lcm(a−1,b), where lcm(a,b) denotes the smallest common multiple, and gcd(a,b) denotes the greatest common divisor of numbers a,b.
Original LaTeX notation
Determine all such pairs pf  positive integers $(a, b)$ such that  $a + b + (gcd (a, b))^ 2 = lcm (a, b) = 2 \cdot  lcm(a -1, b)$, where $lcm (a, b)$ denotes the smallest common multiple, and $gcd (a, b)$ denotes the greatest common divisor of numbers $a, b$.

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Source and history

task_id
203548ef-0141-547b-8ca9-b6c06e999145
task_key
test--203548ef-0141-547b-8ca9-b6c06e999145
task_revision_id
1
config / split
/ test

Official source

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