Re: Solution of problem 1
Posted: Wed Mar 24, 2021 4:55 pm
I am noob in NT. if the answer is wrong please share me the right solution
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Anindya Biswas wrote: ↑Wed Mar 24, 2021 3:26 pmLet $a,b, c, d$ be integers. Show that the product \[(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)\] is divisible by $12$
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wow this was a brain teaser (sorry saw from mathstacks cuz i am noob )Mehrab4226 wrote: ↑Wed Mar 24, 2021 7:44 pmProve that any integer greater than or equal to $7$ can be written as a sum of two relatively prime integers, both greater than $1$.
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There are too many calculations(so a lot of chances for mistakes by me. So I might have skipped some parts. If it is difficult to understand, feel free to ask.Asif Hossain wrote: ↑Fri Mar 26, 2021 7:54 amAn old question nobody answered that so reposted
Problem 9
Find all $a,b \in \mathbb{N}$ such that $y=ax^2+6x+b$ and $y=ax+6$ intersect only once.
Recheck your proof There are solutions for a,b one example is $(a,b)=(2,8)$Mehrab4226 wrote: ↑Fri Mar 26, 2021 2:23 pmThere are too many calculations(so a lot of chances for mistakes by me. So I might have skipped some parts. If it is difficult to understand, feel free to ask.Asif Hossain wrote: ↑Fri Mar 26, 2021 7:54 amAn old question nobody answered that so reposted
Problem 9
Find all $a,b \in \mathbb{N}$ such that $y=ax^2+6x+b$ and $y=ax+6$ intersect only once.
Thank you for pointing that out. I used so the quadratic formula so many times that I accidentally forgot to give the minus before b in a line. I updated my solution.Asif Hossain wrote: ↑Fri Mar 26, 2021 2:39 pmRecheck your proof There are solutions for a,b one example is $(a,b)=(2,8)$Mehrab4226 wrote: ↑Fri Mar 26, 2021 2:23 pmThere are too many calculations(so a lot of chances for mistakes by me. So I might have skipped some parts. If it is difficult to understand, feel free to ask.Asif Hossain wrote: ↑Fri Mar 26, 2021 7:54 amAn old question nobody answered that so reposted
Problem 9
Find all $a,b \in \mathbb{N}$ such that $y=ax^2+6x+b$ and $y=ax+6$ intersect only once.
Problem 10Asif Hossain wrote: ↑Fri Mar 26, 2021 7:54 amAn old question nobody answered that so reposted
Problem 9
Find all $a,b \in \mathbb{N}$ such that $y=ax^2+6x+b$ and $y=ax+6$ intersect only once.