## 14 JunFermat’s Last Theorem

[caption id="attachment_3363" align="alignleft" width="418"] Google Doodle depicting Fermat's Last Theorem[/caption] We can find infinitely many solutions that can solve the equations $$x+y=z$$ and $$x^2+y^2=z^2$$ in integers, but what about the equation $$x^3+y^3=z^3$$ or more generally $$x^n+y^n=z^n$$, where n is an integer greater than 2 and x,y,...

## 06 MayMathletics 2013 (Category IV) - Assam Academy of Mathematics

(Class XI and XII) Marks: 100 Time: 3 Hours [Answer in English. Two students of the group will discuss the solution of the problems and then write the answer in a khata for the group. No third person can help the group to solve the problems.] Answer the following...

## 06 MayMathletics 2013 (Category III) - Assam Academy of Mathematics

(Class IX and X) Marks: 100 Time: 3 Hours [Answer the following questions in English or in mother tongue. Two students of the group will discuss the solutions of the problems and write answer in a khata for the group. No third person can help the group to...

## 06 MayMathletics 2013 (Category II) - Assam Academy of Mathematics

(Class VII and VIII) Marks: 100 = 5X20 Time: 3 Hours [Answer the following questions in English or in mother tongue. Two members of each group will discuss the solutions of the problems and one of them will write the solutions in a khata for the group.] [তলত দিয়া...

## 06 MayMathletics 2013 (Category I) - Assam Academy of Mathematics

(Class V and VI) Marks: 100 = 5X20 Time: 3 Hours [Answer the following questions in English or in mother tongue. Two participants will discuss the solutions of the problems and they will write the answer in a khata for the group. None can help the group in...

## 16 AprThe Number of Solutions of a System of Linear Equations

The standard form of a linear equation in $$n$$ unknowns $$x_1,x_2,\dots ,x_n$$ is $$a_1x_1+a_2x_2+\dots +a_nx_n=b,$$ where $$a_1,a_2,\dots ,a_n$$ and $$b$$ are constants. Here constants mean some real numbers (these constants may come from any number field). A collection of one or more linear equations of same variables is called...

## 06 AprIf p is a prime then √p is irrational

To prove √p is irrational, where p is a prime, we will need the following theorem: Theorem: If $$p$$ is prime then $$p|ab,$$ then $$p|a$$ or $$p|b.$$ Proof: If $$p|a,$$ we are done. So let us assume that $$pmid a.$$ Therefore, $$gcd(p,a)=1.$$ Hence, by Euclid’s lemma, $$p|b.$$...

## 07 FebINMO 2013

The 28th Indian National Mathematical Olympiad (INMO) was held on 3rd February, 2013 across the nation. The questions asked in the exam are provided below. We shall publish solutions to the problems shortly. INMO 2013 [ad#ad-2]...

## 01 Febপেলিনড্ৰম সংখ্যা (Palindrome Number)

যিবোৰ শব্দ, বাক্য বা ছন্দ সচৰাচৰ পঢ়াৰ ধৰণতকৈ বিপৰীত ফালৰ পৰা, অৰ্থাৎ সোঁফালৰ পৰা বাওঁফাললৈ পঢ়িলে একেই হয় সেইবোৰক পেলিনড্ৰম বোলে। যেনে- Refer, level, নৱজীৱন। তথ্য অনুসৰি, মধ্যযুগত ইউৰোপ, আমেৰিকাত পেলিনড্ৰম আৱিস্কাৰ কৰাতো এটি খেলৰ দৰে আছিল আৰু গ্ৰীক, লেটিন আৰু ৰোমান ভাষাত ইয়াৰ চৰ্চা...

## 28 JanFind the Remainder

1) The remainder when $$3^{31}$$ is divided by 5 is A) 2 B) 3 C) 4 D) 1 (Hint: - gcd(3,5)=1 and $$\phi (5)=4,$$ thus $$3^4\equiv 1(mod 5).$$) 2) The reminder when $$5^{99}$$ is divided by 13 is A) 0 B) 8 C) 1 D) 4   3) The reminder when...