BdMO 2017 Dhaka divitional
Forum rules
Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.

 Posts: 21
 Joined: Sat Jan 28, 2017 11:06 pm
BdMO 2017 Dhaka divitional
Two points $A(x_A, y_B), B(x_A+5,y_B+12 )$ are on parabola $5x^2px5y+q=0$ such that $x_A+y_B=5$. How many possible positive integer pairs $(p, q)$ are there where positive integer $q \leq 2050$ ?
 samiul_samin
 Posts: 999
 Joined: Sat Dec 09, 2017 1:32 pm
Re: BdMO 2017 Dhaka divitional
Use Modular Arithmaticsoyeb pervez jim wrote: ↑Wed Mar 28, 2018 8:02 pmTwo points $A(x_A, y_B), B(x_A+5,y_B+12 )$ are on parabola $5x^2px5y+q=0$ such that $x_A+y_B=5$. How many possible positive integer pairs $(p, q)$ are there where positive integer $q \leq 2050$ ?
Answer

 Posts: 21
 Joined: Sat Jan 28, 2017 11:06 pm
Re: BdMO 2017 Dhaka divitional
May be the answer is $21+20=41$
$21$ for $q=5n^{2}2n+22$ ; $20$ for $q=5n^{2}+2n+22$
$21$ for $q=5n^{2}2n+22$ ; $20$ for $q=5n^{2}+2n+22$
 samiul_samin
 Posts: 999
 Joined: Sat Dec 09, 2017 1:32 pm
Re: BdMO 2017 Dhaka divitional
Then my solution is wrong.My solution is too long to postsoyeb pervez jim wrote: ↑Wed Feb 20, 2019 2:12 pmMay be the answer is $21+20=41$
$21$ for $q=5n^{2}2n+22$ ; $20$ for $q=5n^{2}+2n+22$