Discussion Channel for Brilliant Junior NT Contest

The reason behind creating this discussion note , is to keep main contest note clean, the main contest note is getting overcrowded with discussion comments.

Feel free to discuss about problems here.

Here is a link of the contest note.

#NumberTheory

Easy Math Editor

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:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Can someone post a formal, rigorous solution to Q5?

Sharky Kesa - 5 years, 2 months ago

Well , I am also not getting that one :(

A Former Brilliant Member - 5 years, 2 months ago

Solution posted by lakshya sinha is wrong as well as the answer . I am posting the next question (6) and the answer of this question (5)

Shivam Jadhav - 5 years, 2 months ago

sure ...

A Former Brilliant Member - 5 years, 2 months ago

This is the hardest branch of maths I think

Aakash Khandelwal - 5 years, 2 months ago

What does Spagnoletti mean when writing "there are only 2 solutions which are s + r = p"? What is s and what is r and what is the equation we are supposed to be solving? (Since the first is assumed correct for all x if I am reading it right)

Alex Li - 5 years, 2 months ago

Apparently I am just dumb, because I don't understand the next one either - a^x+b^x=2^y 1^1+3^1=2^2 a≠b

Alex Li - 5 years, 2 months ago

Yes probably it is positive integers other than 1. @Sharky Kesa please reply and change the problem title to EPP set 3 #1

A Former Brilliant Member - 5 years, 2 months ago

I will ask this question to him in the main note itself as I am not able to tag him.

A Former Brilliant Member - 5 years, 2 months ago

Everybody please note that , this season is soon going to end...after @Svatejas Shivakumar' s Extra Parti.Prob. set 3 gets solved....Next season will be more interesting ! Brilliant Advanced NT Contest. All the previous contestants take this note.....

@Sharky Kesa , @Shivam Jadhav , @Harsh Shrivastava , @Alex , @Ankit Kumar Jain

A Former Brilliant Member - 5 years, 2 months ago

So soon? Anyways thank you everyone for making this contest a grand success. Had great fun.

A Former Brilliant Member - 5 years, 2 months ago

Thanks for contributing...:) second season will be more interesting and good hope you will enjoy it. Alex and Svatejas...

A Former Brilliant Member - 5 years, 2 months ago

@A Former Brilliant Member – Surely it will be so.

Alex Spagnoletti - 5 years, 2 months ago

@A Former Brilliant Member – Sure it will be. When will season 2 start?

A Former Brilliant Member - 5 years, 2 months ago

Thank you for the contest. It has been a fantastic opportuinity to improve our Number Theory knowledge.

Alex Spagnoletti - 5 years, 2 months ago

After shivam jadhav's problem is solved , I think we must move on to new fresh , note ....

Till Shivam's problem unsolved you can post extra participation problems ......... anybody who wants to ....but only 1 EPP is allowed . per regular question.

Keep this in Mind !!!!

A Former Brilliant Member - 5 years, 2 months ago

I think that you can start note-2 soon. There are well over 100 comments and it is very hard to see to where someone commented.

A Former Brilliant Member - 5 years, 2 months ago

I think we will start the new note after say problem 15 as the contest started just few days back and it will be difficult for some people to start from the second note. The note can be made better if we all delete all the unnecessary comments.

I think that it will be better if every person is allowed to post 1 EPP per regular question.

A Former Brilliant Member - 5 years, 2 months ago

okay !

A Former Brilliant Member - 5 years, 2 months ago

Guys I will be inactive on Brilliant for 6-7 days as I am going on holiday trip....:( :( :( :(

A Former Brilliant Member - 5 years, 2 months ago

@Svatejas Shivakumar , @Sharky Kesa

I still think that there can be some conclusion for EPP problem 1 . We are getting a number which is divisible by 2000 which has one factor which is given number , ...So there can be some relation ...

A Former Brilliant Member - 5 years, 2 months ago

@Sharky Kesa

A Former Brilliant Member - 5 years, 2 months ago

With the question, what you actually want to try to prove is that the expression is divisible by 16 and 125.

Sharky Kesa - 5 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$