Skip over navigation
and
$x^3+y^3 \equiv (x+y)(x^2-xy+y^2)$
Powerful Factors
Age 16 to 18
Challenge Level 
Use the following identities:
$x^2-y^2 \equiv (x-y)(x+y)$and
$x^3+y^3 \equiv (x+y)(x^2-xy+y^2)$
to find the highest power of $2$ and the highest power of $3$ which divide $5^{36}-1$.
You may also like
Code to Zero
Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.
Always Two
Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.
