Perfect Math Tactics
28 HOURS A DAY, 6 DAYS A WEEK
Website Under Construction
OUR GOAL
To use problem-solving tactics to teach the math you are learning while preparing you for upcoming exams. You will learn very efficiently, as if you are studying 28 hours a day, 6 days a week instead of the usual 24/7.
What's a Perfect Number?
A positive integer that is equal to the sum of its divisors, excluding the number itself.
6 = 1 + 2 + 3
28 = 1 + 2 + 4 + 7 + 14
……
$2^{n-1}(2^n – 1)$ is a perfect number where $2^n – 1$ is prime
6 = 1 + 2 + 3
28 = 1 + 2 + 4 + 7 + 14
……
$2^{n-1}(2^n – 1)$ is a perfect number where $2^n – 1$ is prime
$$6=2^1(2^2-1)=1+2+3\\28=2^2(2^3-1)=1+2+3+4+5+6+7\\=1^3+3^3\\496=2^4(2^5-1)=1+2+3+…+29+30+31\\=1^3+3^3+5^3+7^3\\8128=2^6(2^7-1)=1+2+3+…+125+126+127\\=1^3+3^3+5^3+7^3+9^3+11^3+13^3+15^3\\33550336=2^{12}(2^{13}-1)=1+2+3+…+8189+8190+8191\\=1^3+3^3+5^3+…+123^3+125^3+127^3$$
$$6_{10}=2^2+2^1=110_{2}\\28_{10}=2^4+2^3+2^2=11100_{2}\\496_{10}=2^8+2^7+2^6+2^5+2^4=111110000_{2}\\8128_{10}=2^{12}+2^{11}+2^{10}+2^9+2^8+2^7+2^6=1111111000000_{2}$$