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…