## BdMO 2017 Dhaka divitional

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soyeb pervez jim
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 $5x^2-px-5y+q=0$ 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: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### Re: BdMO 2017 Dhaka divitional

soyeb pervez jim wrote:
Wed Mar 28, 2018 8:02 pm
Two points $A(x_A, y_B), B(x_A+5,y_B+12 )$ are on parabola $5x^2-px-5y+q=0$ such that $x_A+y_B=5$. How many possible positive integer pairs $(p, q)$ are there where positive integer $q \leq 2050$ ?
Use Modular Arithmatic

soyeb pervez jim
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 $q=5n^{2}+2n+22$

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### Re: BdMO 2017 Dhaka divitional

soyeb pervez jim wrote:
Wed Feb 20, 2019 2:12 pm
May be the answer is $21+20=41$
$21$ for $q=5n^{2}-2n+22$ ; $20$ for $q=5n^{2}+2n+22$
Then my solution is wrong.My solution is too long to post