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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

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## Comments

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This is a solution using the Euclidean algorithm

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How you can say that $n\geq a$

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Meaning $0$ or $1$.

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Not really though.

Such a condition is satisfied by the integers:

$n = 9, a = 7, b = 13 \text{ and } n = 16, a = 13, b = 21$

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Well - this is out of my league...

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All I can figure out is that $ab = 0 \backslash 1$.

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The problem seems interesting, but way more difficult than it looks! I'll try and tell if I am able to find something(very less probability though).

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Not surprisingly, I could not find a good method. Sorry!

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An approach could be to make a quadratic in $n$ and equating the discriminant greater than 0. Maybe... but I don't see whether it's truly possible

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Doesn't lead to anything sadly

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Yes it doesn't

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I have no idea, @Syed Hamza Khalid.

@Zakir Husain, can you help him out?

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I'm trying right now!!!

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@Mahdi Raza, @Vinayak Srivastava

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@Zakir Husain

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