A point (a, b) is called lucky if it is on the line ax + by =169. For example, the point (12, 5) is lucky because it is on the line 12x+5y=169. What is the square of the maximum possible distance between two lucky points?
Source :Bdmo regional 2020 higher secondary
Search found 71 matches
- Wed Feb 02, 2022 2:18 pm
- Forum: Higher Secondary Level
- Topic: Secondary and Higher Secondary Marathon
- Replies: 128
- Views: 312779
- Tue May 25, 2021 4:43 pm
- Forum: Number Theory
- Topic: Hard Diophantine (maybe)
- Replies: 7
- Views: 12071
Re: Hard Diophantine (maybe)
pythagorean triple? Yeap.(But not so easy to prove).If I remember correctly this diophantine was solved by Sierpinski in 1956 and there is also a conjecture stating that if $a,b,c$ are phythagorean triples then $a^x+b^y=c^z$ has only the solution $(x,y,z)=(2,2,2)$. But sadly nobody could prove it :...
- Mon May 24, 2021 11:12 pm
- Forum: College / University Level
- Topic: All About Fractions
- Replies: 5
- Views: 10748
Re: All About Fractions
Last example is similar to continued fraction maybe
- Mon May 24, 2021 11:10 pm
- Forum: Number Theory
- Topic: Hard Diophantine (maybe)
- Replies: 7
- Views: 12071
Re: Hard Diophantine (maybe)
pythagorean triple?
- Mon May 24, 2021 11:09 pm
- Forum: Social Lounge
- Topic: Struggling with math
- Replies: 6
- Views: 13969
Re: Struggling with math
যদি IMO লক্ষ্য হয় হসচের পড়ায় ক্ষতি হবেই। কজ তুই একদম নতুন।আর তোর যদি প্রাইভেট ইউনিতে পড়ার সামর্থ্য না থাকে তো হসচের পড়া উচিত। আর যদি শখের বশে পড়িস।তো সপ্তাহে ৯/১০ ঘণ্টা ম্যাথই এনাফ।আমি আপাতত থিওরি পড়ি না।
- Sun May 23, 2021 7:08 pm
- Forum: Social Lounge
- Topic: Struggling with math
- Replies: 6
- Views: 13969
Re: Struggling with math
You should focus on HSC.
- Thu May 13, 2021 2:36 pm
- Forum: National Math Camp
- Topic: Problem - 03 - National Math Camp 2021 Mock Exam - "Functional equation, but not functioning well!"
- Replies: 3
- Views: 10816
- Fri May 07, 2021 6:19 pm
- Forum: Algebra
- Topic: A question about FE
- Replies: 9
- Views: 15211
Re: A question about FE
Main problem konta?
- Sun May 02, 2021 6:15 pm
- Forum: Number Theory
- Topic: A Problem from Dustan
- Replies: 4
- Views: 11693
Re: A Problem from Dustan
Solution with some of my friends. As well $r=2$ and there is no solution when $4\leq q$ and $p=q=r$ We will see two cases. Case 1: $q=2$ The equation becomes $p!+4=2^s$ Or,$0+1\cong (-1)^s$ (mod $3$) If, $s$ is odd then it's a contradiction. Let $s=2m$,$m>1$ So, $p!+4=4^m$ If, $p>7$ then L.H.S.$ \co...
- Sun May 02, 2021 2:59 pm
- Forum: Number Theory
- Topic: A Problem from Dustan
- Replies: 4
- Views: 11693
Re: A Problem from Dustan
$p=5$ is also a soln