Mymathware Shafii's math academy

Proof that for any integer $n>1$ the number $n^5+n^4+1$ is not a prime. Simply rewrite $n^5+n^4+1$ as $n^5+n^4+n^3-n^3-n^2-n+n^2+n+1$ Factor out common terms  $n^3(n^…

The product of the third and the sixth terms of an arithmetic sequence is $406$. The ninth term of the sequence divided by the fourth term gives a quotient of $2$ and a …

Find the sum of all natural numbers between $1$ and $1000$ that are not divisible by $13$. Let $S$ be the unknown sum and $M$ multiples of $13$ less than $1000$, then $S…

Find the integer solution $x^2+3x+9=9y^2$.............(1) This is a beautiful quadratic Diophantine's equation that requires an integer solution. So how …

Prove of the Cassini-Samson Identity The Cassini-Samson Identity is an identity that involves the Fibonnaci numbers, it states that $F_{n-1}F_{n+1}-F_{n}^2=(-1)^n$ for $…

If $ab=0$ what is the possible integer value of $a$ and $b$. Answer   The only zero divisor in the Ring of integers is zero. Hence the simplest answer to this question i…

An introduction to numeric palindrome Numeric palindrome or palindromic numbers are numbers that remains the same when its digits are reversed e.g $111,88,151$ and so on…

Largest prime numbers ever printed on the computer has 24 million digits with over $100,000 prize. A portrait of Marin Mersenne and his prime formula Prime numbers are p…

What is the simple proof of Fermat's Last Theorem? There isn't yet a simple proof, that's why it took so long time to be proved, considering the statement of…

The Fermat's last theorem, the exegesis, Andrew Wiles contribution and the quest for a solution. A photo of Andrew Wiles The Fermat's last theorem is a 358 years…

How to proof that $7$ is irreducible $\mathbb{Z}[\sqrt{6}]$, even though $N(7)$ is not prime.  To solve this, lets look at the rules that govern irreducibles in $\mathbb…