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Omni-MATH / There is the number 1 on the board at the beginning. If the number a is written on the board, then we can also write a natural number b such that a+b+1 is a divisor of a²+b²+1. Can…

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problem

There is the number 11 on the board at the beginning. If the number aa is written on the board, then we can also write a natural number bb such that a+b+1a + b + 1 is a divisor of a2+b2+1a^2 + b^2 + 1. Can any positive integer appear on the board after a certain time? Justify your answer.
Plain-text mathematical notation (without MathML)
There is the  number 1 on the board at the beginning. If the number a is written on the board, then we can also write a natural number b such that a+b+1 is a divisor of a²+b²+1. Can  any positive integer appear on the board after a certain time? Justify your answer.
Original LaTeX notation
There is the  number $1$ on the board at the beginning. If the number $a$ is written on the board, then we can also write a natural number $b$ such that $a + b + 1$ is a divisor of $a^2 + b^2 + 1$. Can  any positive integer appear on the board after a certain time? Justify your answer.

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Source and history

task_id
748a4f94-a5c2-5277-b3d0-9fb3eda1cdd3
task_key
test--748a4f94-a5c2-5277-b3d0-9fb3eda1cdd3
task_revision_id
1
config / split
/ test

Official source

initial import